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.)

Solutions

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 1 year ago

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