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Windsor stock has produced returns of 13.8 percent, 11.7 percent, 2.3 percent, -21.4 percent, and 8.9...

Windsor stock has produced returns of 13.8 percent, 11.7 percent, 2.3 percent, -21.4 percent, and 8.9 percent over the past five years, respectively. What is the variance of these returns?C) .020574

I need to know how to solve I have the answer

Expert Solution

First we will calculate the Arithmetic mean as per below:

Formula for Arithmetic Mean is:

Arithmetic Mean (AM) = Sum of the data / No. of data

Sum of the returns = 13.8 + 11.7 + 2.3 + (-21.4) + (8.9) = 15.3

No. of data = 5

Arithmetic Mean = 15.3 / 5 = 3.06 or 0.0306

Steps for calculating variance are:

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

1st: 0.138 - 0.0306 = 0.1074

2nd : 0.117 - 0.0306 = 0.0864

3rd: 0.023 - 0.0306 = -0.0076

4th: -0.214 - 0.0306 = -0.2446

5th: 0.0809 - 0.0306 = 0.0584

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

1st: (0.1074)² = 0.01153476

2nd : (0.0864)² = 0.00746496

3rd: (-0.0076)² = 0.00005776

4th: (-0.2446)² = 0.05982916

5th: (0.0584)² = 0.00341056

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

Sum of squared deviations = 0.01153476 + 0.00746496 + 0.00005776 + 0.05982916 + 0.00341056 = 0.0822972

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 5 here.

Putting the values in the above equation, we get,

Variance = 0.0822972 / 5-1

Variance = 0.0822972 / 4 = 0.020574

jeff jeffy answered 3 months ago

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