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15 April, 07:26

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?

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  1. 15 April, 07:37
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    20.83%

    The basic definition of the standard deviation is the square root of the mean of the squares of the difference from the mean. So let's first calculate the mean:

    (14+9+16+24-40+4) / 6 = 27/6 = 4.5

    Now the mean of the squares of the difference from the mean:

    ((14-4.5) ^2 + (9-4.5) ^2 + (16-4.5) ^2 + (24-4.5) ^2 + (-40-4.5) ^2 + (4-4.5) ^2) / 6

    = (9.5^2+4.5^2+11.5^2+19.5^2 + (-44.5) ^2 + (-0.5) ^2) / 6

    = (90.25 + 20.25 + 132.25 + 380.25 + 1980.25 + 0.25) / 6

    = 2603.5/6

    = 433.9166667

    And finally, the square root. So

    sqrt (433.9166667) = 20.8306665

    So the standard deviation of those returns is 20.83%
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