6six 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

option (C) 22.82 percent

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 =

= 4.5%

Standard deviation =

      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 =

or

Standard deviation = 22.818% ≈ 22.82%

Hence,

The answer is option (C) 22.82 percent

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