Final answer:
The stock's expected return is 3%. The stock's variance is 140%. The stock's standard deviation is approximately 11.83%.
Step-by-step explanation:
To calculate the stock's expected return, we need to find the average (mean) of the annual returns. The sum of the returns is: -6% + (-1%) + (-4%) + 23% = 12%. Divide this sum by the number of returns (4) to get the average: 12%/4 = 3%. So, the stock's expected return is 3%.
To find the variance, we need to calculate the difference between each return and the expected return, square each difference, sum the squared differences, and divide by the number of returns. The squared differences are: (-6% - 3%)^2, (-1% - 3%)^2, (-4% - 3%)^2, and (23% - 3%)^2. The sum of the squared differences is 560. Divide this sum by the number of returns (4) to get the variance: 560/4 = 140%. Therefore, the stock's variance is 140%.
To find the standard deviation, we need to take the square root of the variance. So, the stock's standard deviation is √140% ≈ 11.83%.