Portfolio analysis: You have been given the expected return data shown in the fi
ID: 2710636 • Letter: P
Question
Portfolio analysis:
You have been given the expected return data shown in the first table on three assets -F, G, and H- over the period 2016-2019.
Expected return Asset F
2016 16%,
2017 17%
2018 18%
2019 19%
Asset G
2016 17%
2017 16%
2018 15%
2019 14%
Asset H
2016 14%
2017 15%
2018 16%
2019 17%
Using these assets, you have isolated the three investment alternatives shown in the following table.
Alternative 1- 100% of asset F
Alternative 2 50% of asset F and 50% of asset G
Alternative 3 50% of asset F and 50% of asset H
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?
Explanation / Answer
a. Expected portfolio return:
Alternative 1: 100% Asset F
16%+17%+18%+19%/4=17.5%
Alternative 2: 50% Asset F + 50% Asset G
Asset F Asset G Portfolio Return
Year (wF x kF) + (wG x kG) kp
2016 (16% x .50 = 8.0%) + (17% x .50 = 8.5%) = 16.5%
2017 (17% x .50 = 8.5%) + (16% x .50 = 8.0%) = 16.5%
2018 (18% x .50 = 9.0%) + (15% x .50 = 7.5%) = 16.5%
2019 (19% x .50 = 9.5%) + (14% x .50 = 7.0%) = 16.5%
kp=66/4=16.5%
Alternative 3: 50% Asset F + 50% Asset H
Asset F Asset H Portfolio Return
Year (wF x kF) + (wH x kH) kp
2016 (16% x .50 = 8.0%) + (14% x .50 = 7.0%) 15.0%
2017 (17% x .50 = 8.5%) + (15% x .50 = 7.5%) 16.0%
2018 (18% x .50 = 9.0%) + (16% x .50 = 8.0%) 17.0%
2019 (19% x .50 = 9.5%) + (17% x .50 = 8.5%) 18.0%
kp=66/4=16.5%
b. Standard Deviation:
(1)
(2)
(3)
c. Coefficient of variation: CV =
d. Summary:
kp: Expected Value
of Portfolio skp 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.