Question

1. A firm has the following annual returns for the last five years:

1. 20%
2. 17%
3. 19%
4. -40%
5. 18%

Please calculate the SD and the Mean of the firm for the period in question; in addition, what is the range of values that would fall within:

1. 68% of the time
2. 99% of the time
3. 95% of the time

     Answer: M: 6.8; SD: 26.18

1. -19.38 to 32.98
2. -71.74 to 85.34
3. 45.56 to 59.16

Need explanation for this answer

Answer 1

Solution:

It is given that the last 5 years return are as follows - 20%, 17%, 19%, -40% and 18%

Range of values that would fall within: This can be explained by a normal distribution and the range lies within certain standard deviations.

68% of the time - 68% of the time the value will lie within 1 standard deviation

6.8% - 26.18% to 6.8% + 26.18%

-19.38% to 32.98%

99% of the time- 99% of the time the value will lie within 3 standard deviation

6.8% - 3 * 26.18% to 6.8% + 3 * 26.18%

-71.74% to 85.34%

95% of the time - 95% of the time the value will lie within 2 standard deviation

6.8% -2 * 26.18% to 6.8% + 2 * 26.18%

-45.56% to 59.16%