Question

1. The stocks on ABC Company and XYZ Company have the following returns over the last four years.                                                                                   

Year	ABC returns	XYZ returns
1	-0.2	0.05
2	0.5	0.09
3	0.3	-0.12
4	0.1	0.2

a.   Calculate the average return on ABC.                                                               (1 mark)

b.   Calculate the average return on XYZ.                                                               (1 mark)

c.   Calculate the variance and standard deviation on the ABC returns.   (2.5 marks)

d.   Calculate the variance and standard deviation on the XYZ returns.   (2.5 marks)

e.   Using the coefficient of variation (standard deviation/average return) to compare the two stocks, which stock is preferable?                                                   

Answer 1

Year	ABC returns	XYZ returns
1	-0.2	0.05
2	0.5	0.09
3	0.3	-0.12
4	0.1	0.2

a. Average return on ABC = (-0.2+0.5+0.3+0.1)/4 = 0.175

Average return of ABC = 0.175

b. Average return on XYZ = (0.05+0.09-0.12+0.2)/4 = 0.055

Average return on XYZ = 0.055

c. Variance is calculated using the below formula:

If n is the sample size, then the variance of the sample is calculated using the below formula:

where E[R] is the expected or average return of the asset.

Variance of ABC = [(-0.2-0.175)² + (0.5-0.175)² + (0.3-0.175)² + (0.1-0.175)²]/3 = (0.140625+0.105625+0.015625+0.005625)/3 = 0.2675/3 = 0.089167

We know that standard deviation is the square root of variace. So, Standard deviation of ABC = (0.08917)^1/2 = 0.298608

Varaince of ABC = 0.089167

Standard Deviation of ABC = 0.298608

d. Variance of XYZ = [(0.05-0.055)² + (0.09-0.055)² + (-0.12-0.055)² + (0.2-0.055)²]/3 = 0.017633

Standard deviation of XYZ = (0.017633)^1/2 = 0.132791

Varaince of XYZ = 0.017633

Standard Deviation of XYZ = 0.132791

e. Coefficient of variation of ABC = 0.298608/0.175 = 1.706331

Coefficient of variation of XYZ = 0.132791/0.055 = 2.414374

Stocks with lesser coefficient of variation is more preferable because they have lower standard deviation for unit return. Hence Stock ABC is more preferable.