Question

You are given the returns for the following three stocks:

Year	Stock A			Stock B			Stock C
1	8	%		4	%		-22	%
2	8			11			35
3	8			7			14
4	8			8			9
5	8			10			4

Calculate the arithmetic return, geometric return, and standard deviation for each stock. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

Answer 1

Stock A:

Arithmetic Return = [0.08 + 0.08 + 0.08 + 0.08 + 0.08] / 5
Arithmetic Return = 0.40 / 5
Arithmetic Return = 0.08 or 8.00%

Geometric Return = [(1+0.08) * (1+0.08) * (1+0.08) * (1+0.08) * (1+0.08)]^(1/5) - 1
Geometric Return = 1.469328^(1/5) - 1
Geometric Return = 1.08 - 1
Geometric Return = 0.08 or 8.00%

Variance = [(0.08 - 0.08)^2 + (0.08 - 0.08)^2 + (0.08 - 0.08)^2 + (0.08 - 0.08)^2 + (0.08 - 0.08)^2] / 4
Variance = 0 / 4
Variance = 0.00

Standard Deviation = (0.00)^(1/2)
Standard Deviation = 0.00

Stock B:

Arithmetic Return = [0.04 + 0.11 + 0.07 + 0.08 + 0.10] / 5
Arithmetic Return = 0.40 / 5
Arithmetic Return = 0.08 or 8.00%

Geometric Return = [(1+0.04) * (1+0.11) * (1+0.07) * (1+0.08) * (1+0.10)]^(1/5) - 1
Geometric Return = 1.467427^(1/5) - 1
Geometric Return = 1.0797 - 1
Geometric Return = 0.0797 or 7.97%

Variance = [(0.04 - 0.08)^2 + (0.11 - 0.08)^2 + (0.07 - 0.08)^2 + (0.08 - 0.08)^2 + (0.10 - 0.08)^2] / 4
Variance = 0.0030 / 4
Variance = 0.00075

Standard Deviation = (0.00075)^(1/2)
Standard Deviation = 0.0274 or 2.74%

Stock C:

Arithmetic Return = [(-0.22) + 0.35 + 0.14 + 0.09 + 0.04] / 5
Arithmetic Return = 0.40 / 5
Arithmetic Return = 0.08 or 8.00%

Geometric Return = [(1-0.22) * (1+0.35) * (1+0.14) * (1+0.09) * (1+0.04)]^(1/5) - 1
Geometric Return = 1.360796^(1/5) - 1
Geometric Return = 1.0636 - 1
Geometric Return = 0.0636 or 6.36%

Variance = [(-0.22 - 0.08)^2 + (0.35 - 0.08)^2 + (0.14 - 0.08)^2 + (0.09 - 0.08)^2 + (0.04 - 0.08)^2] / 4
Variance = 0.1682 / 4
Variance = 0.04205

Standard Deviation = (0.04205)^(1/2)
Standard Deviation = 0.2051 or 20.51%