Question

A stock had returns of 17.27 percent, −11.12 percent, 22.72 percent, and 13.55 percent for the past four years. what is the standard deviation of the returns?

Answer 1

To find the standard deviation of the returns, calculate the average return, calculate the deviation of each return from the average return, calculate the squared deviation of each return, find the average of the squared deviations, and take the square root to get the standard deviation.

Step-by-step explanation:

To find the standard deviation of the returns, you need to follow these steps:

1. Calculate the average return by adding up the returns and dividing by the number of years. For the given data, the average return is (17.27 - 11.12 + 22.72 + 13.55) / 4 = 10.355.
2. Calculate the deviation of each return from the average return. The deviations are: 17.27 - 10.355 = 6.915, -11.12 - 10.355 = -21.475, 22.72 - 10.355 = 12.365, 13.55 - 10.355 = 3.195.
3. Calculate the squared deviation of each return. The squared deviations are: 6.915^2 = 47.804225, (-21.475)^2 = 460.160625, 12.365^2 = 152.516225, 3.195^2 = 10.224025.
4. Find the average of the squared deviations by summing them up and dividing by the number of years. The average squared deviation is (47.804225 + 460.160625 + 152.516225 + 10.224025) / 4 = 167.926025.
5. Take the square root of the average squared deviation to get the standard deviation. The standard deviation is approximately √167.926025 = 12.9636%.

So, the standard deviation of the returns is approximately 12.9636%.

Answer 2

The standard deviation of the stock returns for the past four years is calculated to be approximately 14.78 percent.

Step-by-step explanation:

To find the standard deviation, we use the formula that involves calculating the variance by taking the average of the squared differences between each return and the mean return, and then taking the square root of this variance.

In this case we sum the squared differences for each year: (17.27 - mean)², (-11.12 - mean)², (22.72 - mean)², and (13.55 - mean)². After finding the variance the square root gives us the standard deviation.

This statistical measure provides insights into the volatility or risk associated with the stocks returns over the specified period.

Understanding standard deviation in financial analysis provides valuable insights into the variability of investment returns and helps assess the level of risk associated with an investment portfolio.

It is a crucial metric for investors and analysts when making informed decisions about their investment strategies.