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Over the past five years, a stock produced returns of 14%, 22%, -16%, 4%, and 11%....

Over the past five years, a stock produced returns of 14%, 22%, -16%, 4%, and 11%. If the returns are normally distributed, what is the probability that an investor in this stock will NOT lose more than 7.4% nor earn more than 21.4% in any one given year? (Hint: Find average return and standard deviation first.)

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Expert Solution

Year Return (%)
1 14
2 22
3 -16
4 4
5 11
Description Value Comments
Average 7 Sum of returns (35) / no. of returns (5)
Standard Deviation 12.86856635 stdev.p formula for returns in excel

In order to calculate probability of specific returns, we will determine the Z score using the below formula and then reference the Z score in the Z table to find the corresponding P value.

Z Score = (X-Mean) / Standard Deviation; where X is the random value

X < or = -7.4
Z score (using above formula) -1.12
Referencing in z score table we have P value of 0.1314 or 13.14%

Probability of return less than -7.4% = 13.14%

X > or = 21.4
Z score (using above formula) 1.12
Referencing in z score table we have P value of 0.1314 or 13.14%

Probability of return greater than 21.4% = 13.14%

Probability of return not less than -7.4% nor greater than 21.4% = Total probability - Probability of return less than -7.4% - Probability of return greater than 21.4% = [1 - 0.134 - 0.134)] = 0.732 or 73.2%

jeff jeffy answered 2 years ago
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