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10 August, 20:14

Over the past four years, a stock produced returns of 14 percent, 22 percent, 6 percent, and - 19 percent. What is the approximate probability that an investor in this stock will not lose more than 30 percent nor earn more than 41 percent in any one given year

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  1. 10 August, 21:09
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    Probability range is 82%

    Explanation:

    To get the probability we need to calculate the mean and standard deviation of the returns.

    The average return on the stock for the period of 4 years is

    Average return = (0.14 + 0.22 + 0.06 - 0.19) : 4

    Average return = 0.0575 = 5.75%

    Total squared deviation = (0.14 - 0.0575) ^2 + (0.22 + 0.0575) ^2 + (0.06 - 0.0575) ^2 + (-0.19 - 0.0575) ^2

    Total squared deviation = 0.0681 + 0.0264 + 0.00000625 + 0.0613

    Total squared deviation = 0.1558

    Standard deviation = √ (0.1558) : (4 - 1)

    Standard deviation = 0.2279 = 22.79%

    Range = 5.75 ± 22.79 = - 17.04 to 28.54

    Probability range is 82%
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