Final answer:
To find the standard deviation of a set of numbers, we need to calculate the mean, subtract the mean from each number, square each difference, find the mean of the squared differences, and take the square root to get the standard deviation. In this case, the standard deviation is 0.
Step-by-step explanation:
To find the standard deviation of a set of numbers, we need to follow these steps:
- Calculate the mean of the data set.
- Subtract the mean from each number in the data set.
- Square each of these differences.
- Find the mean of these squared differences.
- Take the square root of the mean of the squared differences to find the standard deviation.
In this case, since we have three one-year returns of -5, the data set is {-5, -5, -5}. The mean is calculated by adding up all the values and dividing by the number of values: (-5 + -5 + -5) / 3 = -5.
To calculate the standard deviation, we follow the steps outlined above. Subtracting the mean from each number gives us {-5 - (-5), -5 - (-5), -5 - (-5)} = {0, 0, 0}. Squaring each of these differences gives us {0^2, 0^2, 0^2} = {0, 0, 0}. Finding the mean of the squared differences gives us (0 + 0 + 0) / 3 = 0. Finally, taking the square root of the mean of the squared differences gives us √0 = 0.
Therefore, the standard deviation for a security with three one-year returns of -5 is 0.