Final answer:
The standard deviation of the stock's returns over the past three years is calculated by first finding the mean, then the squared deviations from the mean, and finally taking the square root of the average of the squared deviations. The standard deviation, in this case, is 16.75%.
Step-by-step explanation:
The question asks for the standard deviation of the returns of a stock over a three-year period. To calculate the standard deviation, we must first compute the mean (average) of the returns and then determine how much each year's return deviates from that mean. After summing the squared deviations and dividing by the number of observations minus one to get the variance, we take the square root of the variance to obtain the standard deviation.
The mean return is calculated as follows:\[(18.19 + (-7.51) + 23.96) / 3 = 11.5467\%\]
The deviations from the mean are:\[18.19 - 11.5467 = 6.6433\],\[-7.51 - 11.5467 = -19.0567\], and \[23.96 - 11.5467 = 12.4133\].
Now, we square each deviation:\[6.6433^2 = 44.1337\],\[-19.0567^2 = 363.1589\],\[12.4133^2 = 154.0903\].
Then we sum the squared deviations:\[44.1337 + 363.1589 + 154.0903 = 561.3829\] and divide by the number of years minus one (n-1), which in this case is 2:\[561.3829 / 2 = 280.6915\]. This is the variance.
The square root of the variance, which is the standard deviation, is:\[\sqrt{280.6915} = 16.75\%\].
Therefore, the correct answer is 16.75%.