Question

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A stock had returns of 8 percent, –8 percent, 3 percent, and 14 percent over the...

A stock had returns of 8 percent, –8 percent, 3 percent, and 14 percent over the past 4 years. What is the standard deviation of this stock for the past four years?

Multiple choice

16.1 percent
4.7 percent
9.3 percent
4.3 percent

Solutions

Expert Solution

Option (c) is correct

First we will calculate the Arithmetic mean return as per below:

Formula for Arithmetic Mean is:

Arithmetic Mean (AM) return = Sum of returns / No. of returns

Sum of the returns = 8 + (-8) + 3 + 14 = 17

No. of data = 4

Arithmetic Mean return = 17 / 4 = 4.25

Steps for calculating standard deviation are:

First we will calculate the deviation of returns from the mean return value as per below:

1st: 8 - 4.25 = 3.75

2nd : - 8 - 4.25 = -12.25

3rd: 3 - 4.25 = -1.25

4th: 14 - 4.25 = 9.75

In the next step, we will square the deviations computed above, as per below:

1st: (3.75)² = 14.0625

2nd : (-12.25)² = 150.0625

3rd: (-1.25) = 1.5625

4th: (9.75)² = 95.0625

In the next step we will add up the values calculated above:

Sum of squared deviations = 14.0625 + 150.0625 + 1.5625 + 95.0625 = 260.75

In the next step we will calculate the variance by the following formula:

Variance = Sum of squared deviations / N- 1

where, N is the no. of data, which is 4 here.

Putting the values in the above equation, we get,

Variance = 260.75 / 4 -1

Variance = 260.75 / 3 = 86.92

In the final step, we will square root the variance calculated above to find the standard deviation:

Standard deviation = (86.92)^1/2 = 9.3

jeff jeffy answered 3 weeks ago

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