Question

The last four years of returns for a stock are as follows: Year 2 Return -3.6% 28.5% 11.8% 3.8% a. What is the average annual return? b. What is the variance of the stock's returns? c. What is the standard deviation of the stock's returns? a. What is the average annual return? The average return is%. (Round to two decimal places.)

Answer 1

Answer

1. Average annual return (X̅) = 40.5/4

= 10.13%

2. Variance of the stock return      =568.83/4

=142.21

3. standard deviation of the stock return=
   /142.21
   

= 11.93%

Working Notes:

year	X	(x-x̅)	(x-x̅)2
1	-3.6	(-3.6)-10.13=-13.73	(-13.73)2=188.51
2	28.5	28.5-10.13=18.37	18.372=337.46
3	11.8	11.8-10.13=1.67	1.672=2.79
4	3.8	3.8-10.13=-6.33	(-6.33)2=40.07
Total	40.5		568.83

Where X = Return for a stock

x̅= Average of the return

= (total return) ÷ Number of years

= (40.5) ÷ 4

= 10.13%

Variance of the stock return = ( ∑(x-x̅)² ) ÷ Number of years

                                                = 568.83 ÷ 4

                                                =142.21

Standard deviation of the stock returns (SD)

Σα 2 SD

=

/varianceof the stock return

=

/142.21

=11.93%