A Canadian common stock had the following rates of return in the past four years: 7%, 8%, -2%and 11%. The standard deviation (rounded to one decimal) for the rate of return over this 4-yearperiod is
A) 6.2
B) 4.8
C) 5.6
D) 5.3

Question

Quizplus · Accepted Answer

To calculate the standard deviation, we first need to find the average rate of return (also known as the expected return). 
Average return = (7% + 8% - 2% + 11%) / 4 = 6%

Next, we need to calculate the deviation for each year by subtracting the average return from the actual return. 
Deviation of year 1 = 7% - 6% = 1%
Deviation of year 2 = 8% - 6% = 2%
Deviation of year 3 = -2% - 6% = -8%
Deviation of year 4 = 11% - 6% = 5%

Then, square each deviation: 
1%² = 0.01
2%² = 0.04
(-8%)² = 0.64
5%² = 0.25

Add up the squared deviations: 
0.01 + 0.04 + 0.64 + 0.25 = 0.94

Divide the sum of squared deviations by the number of years minus 1 (n-1): 
0.94 / 3 = 0.313333333

Take the square root of the result to get the standard deviation: 
√0.313333333 ≈ 0.5608 ≈ 5.6% (rounded to one decimal)

Therefore, the answer is choice C (5.6)

A Canadian Common Stock Had the Following Rates of Return