Question

A stock you are looking at has generated the following annual returns: 13.6%, -12.1% and 7.6%. What was the standard deviation of its returns? Answer in percent, rounded to two decimal places (e.g., 4.32% = 4.32).

Answer 1

Steps in calculation of standard deviation:

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 = 13.6 + (-12.1) + 7.6 = 9.1

No. of data  = 3

Arithmetic Mean = 9.1 / 3 = 3.03

Steps for calculating standard deviation are:

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

1st: 13.6 - 3.03 = 10.57

2nd : -12.1 - 3.03 = -15.13

3rd: 7.6 - 3.03 = 4.57

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

1st:  (10.57)² = 111.7249

2nd : (-15.13)² = 228.9169

3rd : (4.57)² = 20.8849

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

Sum of squared deviations = 111.7249 + 228.9169 + 20.8849 = 361.5267

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 3 here.

Putting the values in the above equation, we get,

Variance = 361.5267 / 3-1

Variance = 361.5267 / 2 = 180.76335

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

Standard deviation = (180.76335)^1/2 = 13.44%