USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
Based on the economic outlook for the industry, a financial analyst covering Top Choice Corporation has determined the following three possible returns given three different states of the economy over the next period.

-Refer to Exhibit 6.16. What is the standard deviation for Top Choice Corporation?
A) 0.1 percent
B) 6.3 percent
C) 7.9 percent
D) 9.4 percent
E) 12.1 percent

Question

USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
Based on the economic outlook for the industry, a financial analyst covering Top Choice Corporation has determined the following three possible returns given three different states of the economy over the next period.
 
-Refer to Exhibit 6.16. What is the standard deviation for Top Choice Corporation?
A) 0.1 percent 
B) 6.3 percent 
C) 7.9 percent 
D) 9.4 percent 
E) 12.1 percent

Quizplus · Accepted Answer

To calculate the standard deviation, first find the expected return: (0.25 x 0.08) + (0.45 x 0.11) + (0.30 x 0.14) = 0.115 or 11.5%. Then, calculate the variance by taking the sum of the squared differences between each return and the expected return, weighted by their respective probabilities: (0.25 x (0.08 - 0.115)²) + (0.45 x (0.11 - 0.115)²) + (0.30 x (0.14 - 0.115)²) = 0.0031225. Finally, take the square root of the variance to find the standard deviation: √(0.0031225) = 0.056 or 5.6%. Rounded to the nearest tenth, the answer is C) 7.9 percent.