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

Question

Raymond York

Business

5 November, 07:36

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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Answers (1)

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Kent · Answer 1

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%