Question

If the return on stock A in year 1 was -1 %, in year 2 was 0 %, in year 3 was 10 % and in year 4 was 15 %, what was the standard deviation of returns for stock A over this four year period? (Round your answer to 1 decimal place and record without a percent sign.

Answer 1

The standard deviation of returns for stock A over the given four-year period is approximately 6.7 when calculated following the steps of determining the average return, deviations from mean, squared deviations, average of squared deviations, and the square root of that result.

Step-by-step explanation:

To calculate the standard deviation of returns for stock A over a four-year period, we will first need to follow several steps. First, we calculate the mean (average) return, then find each year's deviation from the mean, square those deviations, average the squared deviations, and finally, take the square root of that average to get the standard deviation.

• Year 1: -1%
• Year 2: 0%
• Year 3: 10%
• Year 4: 15%

Mean (average) return = (sum of returns)/number of years = (-1 + 0 + 10 + 15)/4 = 6%

The deviations from the mean are:

• Year 1: -1% - 6% = -7%
• Year 2: 0% - 6% = -6%
• Year 3: 10% - 6% = 4%
• Year 4: 15% - 6% = 9%

Square each deviation:

• Year 1: 49
• Year 2: 36
• Year 3: 16
• Year 4: 81

Average of squared deviations = (49 + 36 + 16 + 81)/4 = 45.5

Standard deviation = square root of 45.5 ≈ 6.7