Question

6 Six years ago, you purchased 100 shares of LIT stock. The annual returns have been 14 percent, 9 percent, 16 percent, 24 percent,- 40 percent, and 4 percent, respectively for those six years. What is the standard deviation of these returns?A. 20.02 percentB.20.67 percentC. 22.82 percentD.25.56 percentE. 26.04 percent

Answer 1

option (C) 22.82 percent

Step-by-step explanation:

Data provided in the question:

Time period, n = 6 years

Annual returns each year: 14%, 9% , 16% , 24%, -40% , 4%

Now,

The average return, Mean =
`(14\% + 9\% + 16\% + 24\% - 40\% + 4\%)/(6)`

= 4.5%

Standard deviation =
`\sqrt{\frac{\textup{ (Return-mean)}^2}{n-1}}`

Return (return-mean)²

14 (14-4.5)² =90.25

9 (9-4.5)² =20.25

16 (16-4.5)² =132.25

24 (24-4.5)² =380.25

-40 (-40-4.5)² =1980.25

4 (4-4.5)² =0.25

=========================================

∑(return-mean)² = 2603.5%

Therefore,

Standard deviation =
`\sqrt{(2603.5\%)/(6-1)}`

or

Standard deviation = 22.818% ≈ 22.82%

Hence,

The answer is option (C) 22.82 percent