Question

If the return on stock A in year 1 was 18%, in year 2 was 0%, in year 3 was −5% and in year 4 was 7%, 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. If your final answer is negative, place a minus sign before the number with no space between the sign and the number).

Answer 1

To calculate the standard deviation of returns for stock A over the four-year period, you need to calculate the average return, find the differences from the average, square the differences, sum them up, divide by the number of years, and take the square root. In this case, the standard deviation of returns for stock A is approximately 8.6%.

Step-by-step explanation:

To calculate the standard deviation of returns for stock A over the four-year period, you need to follow these steps:

1. Calculate the average return for stock A over the four years by summing the returns in each year and dividing by 4.
2. Calculate the difference between each year's return and the average return.
3. Square each difference and sum them up.
4. Divide the sum of squared differences by 4.
5. Take the square root of the result to get the standard deviation.

In this case, the average return is (18% + 0% + (-5%) + 7%)/4 = 5%.

The differences from the average are (18% - 5%), (0% - 5%), (-5% - 5%), and (7% - 5%).

Squaring each difference gives 169, 25, 100, and 4.

The sum of squared differences is 169 + 25 + 100 + 4 = 298.

Dividing by 4 gives 74.5.

Taking the square root gives a standard deviation of √74.5 ≈ 8.6%.