Question

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

Answer 1

Answer:

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%