Historically,the average arithmetic return of Hypothetically Prosperous Company has been 16% while the average geometric return has been 14%.If the returns have been normally distributed,the variance of returns of this stock has been _________.

Question

Quizplus · Accepted Answer

The difference between the average arithmetic return and the average geometric return is attributable to compounding. The formula for approximate variance using arithmetic return and geometric return is:

Variance = (average arithmetic return - average geometric return)^2 - (0.5 * standard deviation)^2

Substituting the given values,

Variance = (16% - 14%)^2 - (0.5 * standard deviation)^2

Solving for standard deviation,

14% = 0.5 * standard deviation * sqrt(3)

standard deviation = 0.3229

Substituting the value of standard deviation in the original equation,

Variance = (16% - 14%)^2 - (0.5 * 0.3229)^2 = 4%

Therefore, the variance of returns of this stock has been 4%.

Historically,the Average Arithmetic Return of Hypothetically Prosperous Company Has Been