Question

1. . You intend to make an investment in one stock and have the following stocks to choose from:

Stock	Expected Return	Standard Deviation
A	20% p.a.	10% p.a.
B	30% p.a.	50% p.a.
C	15% p.a.	12% p.a.
D	20% p.a.	15% p.a.
E	35% p.a.	40% p.a.
F	25% p.a.	15% p.a.

Since every person’s preferred investment will differ, depending on their level of risk aversion, we cannot say for certain which stock you will choose. The risk-return characteristics of some stocks, however, clearly dominates others. Begin by plotting each stock on a graph with risk (standard deviation) on the horizontal axis and expected return on vertical axis. Just plot a single point for each stock.

a. If you had to choose just between stocks A and D, which dominates? Explain.

b. If you had to choose just between stocks D and E, which dominates? Explain.

c. If you had to choose just between stocks B and E, which dominates? Explain.

d. If you had to choose just between stocks A and C, which dominates? Explain.

e. If you had to choose just between stocks A and F, which dominates? How about E and F? how about C and D? Explain.

Answer 1

The plot of the risk & return is shown in the image below:

a) Stock A . We can see that A and D provide the same return , But D has higher risk of 15%. So A lies on the efficient frontier and D lies below it . An investor will prefer investing in A since it gives same returns at lower risk.

b) Stock E .We have seen in the previous question, that D does not lie on the efficient Frontier. So We have to choose Stock E .

c) Stock E .We can see that the return for B is 30% which is lesser than that of E (35%). Also The risk of B is 50% which is more than the risk of E (40%) . So B does not lie on the efficient frontier. An investor will chosse E since it gives higher return at lesser risk.

d) Stock A .C has lower returns (15%) than A(20%) at higher risk . So A dominates as it lies on the efficient frontier by providing higher returns at lower risk.

e) For this question, we need to find the coefficient of variation(CV) for each stock. The CV provides a measure of the risk return tradeoff as it gives the information about the dispersion of data from the mean

Coefficent of Variation (CV) of Stock A = Std dev / Expected return = 10/20 = 0.5

Coefficent of Variation (CV) of Stock F = Std dev / Expected return = 15/25 = 0.6

Since CV of stock A is lower , It provides a higher value of return per unit of risk.So we prefer Stock A

Coefficent of Variation (CV) of Stock E = Std dev / Expected return = 40/35 = 1.14

Coefficent of Variation (CV) of Stock F = Std dev / Expected return = 15/25 = 0.6

Since CV of stock F is Lower , It provides a higher value of return per unit of risk.So we prefer Stock F

Coefficent of Variation (CV) of Stock C = Std dev / Expected return = 12/15 = 0.8

Coefficent of Variation (CV) of Stock D = Std dev / Expected return = 15/20 = 0.75

Since CV of stock D is Lower , It provides a higher value of return per unit of risk.So we prefer Stock D