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

Alternative 2: 50% Asset F + 50% Asset G

Asset F Asset G Portfolio Return
Year (wF x kF) + (wG x kG) kp

2001 (16% x .50 = 8.0%) + (17% x .50 = 8.5%) = 16.5%
2002 (17% x .50 = 8.5%) + (16% x .50 = 8.0%) = 16.5%
2003 (18% x .50 = 9.0%) + (15% x .50 = 7.5%) = 16.5%
2004 (19% x .50 = 9.5%) + (14% x .50 = 7.0%) = 16.5%

Alternative 3: 50% Asset F + 50% Asset H

Asset F Asset H Portfolio Return
Year (wF x kF) + (wH x kH) kp

2001 (16% x .50 = 8.0%) + (14% x .50 = 7.0%) 15.0%
2002 (17% x .50 = 8.5%) + (15% x .50 = 7.5%) 16.0%
2003 (18% x .50 = 9.0%) + (16% x .50 = 8.0%) 17.0%
2004 (19% x .50 = 9.5%) + (17% x .50 = 8.5%) 18.0%

b. Standard Deviation:
(1)

(2)

(3)

c. Coefficient of variation: CV =

d. Summary:

kp: Expected Value
of Portfolio kp CVp

Alternative 1 (F) 17.5% 1.291 .0738
Alternative 2 (FG) 16.5% -0- .0
Alternative 3 (FH) 16.5% 1.291 .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.