Question

A stock produced returns of 14 percent, 17 percent, and −1 percent over three of the past four years, respectively. The arithmetic average for the past four years is 6 percent.

Show your work here (please 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 work below please).

Answer 1

Given:

Year	Return
1	14%
2	17%
3	-1%
4	?

Arthemetic average of returns = 6%

Step 1 : Calculation of return of 4th year

Let the return in 4th year be x

Average returns = Sum of returns / N
where N = Number of years

6% =(14+ 17 +(-1) + x) / 4

6 *4 = 30 + x

x = 24 -30

x = -6 %

Return in 4th year = -6%

Step 2 : Calculation of Geometric Mean (GM)

Year	Return
1	14%
2	17%
3	-1%
4	-6%

where, r1, r2,..., rn =  returns of respective periods
N = Number of years

G.M. = 1.055513 - 1

G.M.  = 0.055513 or 5.55%

Step 3  : Calculation of Standard Deviations ()

Year	Return	Deviations	Deviation^2
1	14%	0.08	0.0064
2	17%	0.11	0.0121
3	-1%	-0.07	0.0049
4	-6%	-0.12	0.0144
		Total	0.0378

where deviations = Return - Average Return (given = 6%)
N = Number of years

or 9.72%

Standard deviation = 9.72%