P5–13 Portfolio analysis You have been given the return data shown in the first table on
three assets—F, G, and H—over the period 2007–2010. Using these assets, you have
isolated the three investment alternatives shown in the following table: a. Calculate the
expected return over the 4-year period for each of the three alternatives. b. Calculate the
standard deviation of returns over the 4-year period for each of the three alternatives. c.
Use your findings in parts a and b to calculate the coefficient of variation for each of the
three alternatives. d. On the basis of your findings, which of the three investment
alternatives do you recommend? Why?
a.
Expected portfolio return:
Alternative 1: 100% Asset F
kp 
16%  17%  18%  19%
 17.5%
4
Alternative 2: 50% Asset F + 50% Asset G
Year
Asset F
(wF x kF)
+
Asset G
(wG x kG)
2001
2002
2003
2004
(16% x .50 = 8.0%)
(17% x .50 = 8.5%)
(18% x .50 = 9.0%)
(19% x .50 = 9.5%)
+
+
+
+
(17% x .50 = 8.5%)
(16% x .50 = 8.0%)
(15% x .50 = 7.5%)
(14% x .50 = 7.0%)
kp 
Portfolio Return
kp
=
=
=
=
16.5%
16.5%
16.5%
16.5%
66
 16.5%
4
Alternative 3: 50% Asset F + 50% Asset H
Year
Asset F
(wF x kF)
+
Asset H
(wH x kH)
2001
2002
2003
2004
(16% x .50 = 8.0%)
(17% x .50 = 8.5%)
(18% x .50 = 9.0%)
(19% x .50 = 9.5%)
+
+
+
+
(14% x .50 = 7.0%)
(15% x .50 = 7.5%)
(16% x .50 = 8.0%)
(17% x .50 = 8.5%)
kp 
66
 16.5%
4
( ki  k ) 2
Standard Deviation: kp  
i 1 ( n  1)
n
b.
(1)
Portfolio Return
kp
15.0%
16.0%
17.0%
18.0%
F 
F 
(16.0%  17.5%)
(-1.5%)
2
 (17.0%  17.5%) 2  (18.0%  17.5%) 2  (19.0%  17.5%) 2
4 1
2
 (0.5%) 2  (0.5%) 2  (1.5%) 2
3
F 
(2.25%  0.25%  0.25%  2.25%)
3
F 
5
 1.667  1.291
3
(2)
(16.5%  16.5%)
FG 
(0)
FG 
2
2


 (16.5%  16.5%) 2  (16.5%  16.5%) 2  (16.5%  16.5%) 2
4 1
 (0) 2  (0) 2  (0) 2
3


FG  0
(3)
FH 
FH 
FH 
FH 
c.
 (15.0%  16.5%)
(1.5%)
2
2
 (16.0%  16.5%) 2  (17.0%  16.5%) 2  (18.0%  16.5%) 2 
4 1
 (0.5%) 2  (0.5%) 2  (1.5%) 2
3

(2.25  .25  .25  2.25)
3
5
 1.667  1.291
3
Coefficient of variation: CV
CVF 
1.291
 .0738
17.5%
CVFG 
0
0
16.5%
=
k  k
CVFH 
d.
1.291
 .0782
16.5%
Summary:
Alternative 1 (F)
Alternative 2 (FG)
Alternative 3 (FH)
kp: Expected Value
of Portfolio
kp
17.5%
16.5%
16.5%
1.291
-01.291
CVp
.0738
.0
.0782
Since the assets have different expected returns, the coefficient of variation should
be used to determine the best portfolio. Alternative 3, with positively correlated
assets, has the highest coefficient of variation and therefore is the riskiest.
Alternative 2 is the best choice; it is perfectly negatively correlated and therefore
has the lowest coefficient of variation.