Portfolio analysis You have been given the expected return data shown in the fir
ID: 2457035 • 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
Year Asset F Asset G Asset H
2016 16% 17% 14%
2017 17 16 15
2018 18 15 16
2019 19 14 17
Alternative Investment
1 100% of asset F
2 50% of asset F and 50% of asset G
3 50% of asset F and 50% of asset H
Asset
Expected
return, r
Risk (standard
deviation), sr
V 8% 5%
W 13 10
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?
Explanation / Answer
a. Expected portfolio return: Alternative 1: 100% Asset F
kp=(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
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%
kp=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%
kp=(15+16+17+18)/4=16.5%
b. standard deviation
altr 1:1.291
altr 2: 0
altr 3: 1.291
c. Coefficient of variation: CV
altr 1:0.0738
altr 2: 0
altr 3: 0.0782
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.