Question

A stock produced returns of 14 percent, 17 percent, and −10 percent over three of the past four years, respectively. The arithmetic average for the past four years is 6 percent.

Show you work here (be as detailed and organized as possible):

1. What is the missing return (i.e., the return in the fourth year)?

2. What is the geometric average return over the four years?

3. What is the standard deviation of returns of the stock? Show your work clearly below.

Answer 1

1)

0.06 = (0.14 + 0.17 - 0.1 + Missing return) / 4

0.24 = 0.14 + 0.17 -0.1 + Missing return

Missing return = 0.03 or 3.00%

2)

Geometric average = [(1 + R1)(1 + R2)(1 +R3)(1 + R4)]^1/n - 1

Geometric average = [(1 + 0.14)(1 + 0.17)(1 - 0.1)(1 + 0.03)]^1/4 - 1

Geometric average = [1.236433]^1/4 - 1

Geometric average = 1.0545 - 1

Geometric average = 0.0545 or 5.45%

3)

Standard deviation = {[(0.14 - 0.06)^2 + (0.17 - 0.06)^2 + (-0.1 - 0.06)^2 + (0.03 - 0.06)^2] / 4 - 1}^1/2

Standard deviation = {[0.0064 + 0.0121 + 0.0256 + 0.0009] / 3}^1/2

Standard deviation {0.015}^1/2

Standard deviation = 0.1225 or 12.25%