Chapter 6
Exercise 1
Solution to Exercise 1 (a)
(i)
 
1 A 2 B E R  16% for all correlations
p
3
3
Sp2 
 13 
2
 8 2
 3
 2
2
16 2
 2.8.16
1 1

3 2
where    1,0,0.3 or  0.8
Sp  8.0%,11.0%, 11.7%, 8.7%
(ii)
 
1 A 1 B E R  15%
p
2
2
Sp2 
 12
2
 8 2
 
 1
2
2
16 2
 2.8.16
1 1

2 2
 2.8.16
2 1

3 3
where    1,0,0.3 or  0.8
Sp  4.0%,8.9%, 10.0%, 5.4%
(iii)
 
2 A 1 B E R  14%
p
3
3
 3
Sp2  2
2
 8 2
 
 1
3
2
16 2
where    1,0,0.3 or  0.8
Sp  0%,7.5%, 8.6%, 3.4%
Solution to Exercise 1 (a)
20
B
18
C
16
D
14
A
E(Rp)
12
10
8
6
4
2
0
4
2
0
10
8
6
12
14
16
Sp
(i)
The highest expected return will be 100% in B. However the
highest expected return given the risk in the diagram is point C,
E(RP) = 16%, Sp = 8%.
(ii)
The minimum risk is point D, E(RP) = 14%, Sp = 0%.
Exercise 2
Solution to Exercise 2 (a)
(i)
Equal X and Y
 
E Rp
 12.375%
Sp2 
 12
Sp  7.9%
2
 7.8 2   12  11.7 2  2.
2
2 1
.11.7.7.8.0.3
3 3
18
(ii)
Equal X and Z
 
E Rp
 14.1%
Sp2 
 12
2
 7.8 2   12  17.6 2  2.
2
1 1
.7.8.17.6.0.9
2 2
Sp  11.6%
(iii)
Equal Y and Z
 
E Rp
 15.9%
Sp2 
 12
2
Sp  11.0%
11.7 2   13  17.6 2  2.
2
1 1
.11.7.0.7.6.0.10
2 2
Solution to Exercise 2 (b)
The standard deviation to the equal YZ portfolio is less than the risk of the XZ
portfolio because of the lower correlation.
Solution to Exercise 2 (c)
Equal X,Y, Z
 
E Rp  1 10.5  14.25  17.60 
3
 14.1%
Sp2 
 13  7.8    13   11.7    13  17.60 
2
1
3
1
2
3
1
2
3
2
2
2
2
2
2
1
. 7.8.11.7.0.3
3
1
.7.8.17.6.0.9
3
1
11.7.17.6.0.1
3
Sp  11.7%
The expected return is very slightly higher than for the XZ combination as is
the standard deviation of returns. Adding Y does little to improve the risk
return tradeoff.
Exercise 3
Solution to Exercise 3 (a)
E R   12%
Sp2 
 12
Sp  6.0%
2
112   12   23 2  2.
2
1 1
.11.2.3.  1
2 2
Solution to Exercise 3 (b)
WSp  1 W  SQ  0
Sp  0
11W  1 W  23  0
W  0.67
One third and two third of gives a perfectly hedged portfolio (with an ECR) of
1/3 x 9 + 2/3 x 15 = 13%
Solution to Exercise 3 (c)
18
15
Q (23,15)
E(Rp)
12
(0,13)
P (9,11)
(6,12)
9
6
3
0
0
3
6
9
12
15
18
21
24
Sp
Solution to Exercise 3 (d)
Options and futures can be structured to be negatively correlated with the
underlying security.
Exercise 4
Solution to Exercise 4 (a)
Sp2 
 13  150   13  150   13 
Sp  7.1%
2
2
2
2
2
150 
 50
27
Solution to Exercise 4 (b)
 
E Rp
 15%
Sp2   0.4  150    0.4  150    0.2  150
2
2
2
2
Sp  7.3%
Solution to Exercise 4 (c)
The minimum risk portfolio will have equal proportions in J, K and L.
Solution to Exercise 4 (d)
Yes, as she would not sacrifice return.