question archive A stock had returns of 5, 14, 11, -8, and 6 percent over the past 5 years
A stock had returns of 5, 14, 11, -8, and 6 percent over the past 5 years
Subject:FinancePrice:3.86 Bought5
A stock had returns of 5, 14, 11, -8, and 6 percent over the past 5 years. The standard deviation for this stock is:
a. 9.68%
b. 7.74%
c. 8.44%
d. 7.49%
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Option C
8.44%
Average return (AR) is computed using the equation given below:
AR = {Return of year 1 + Return of year 2 + Return of year 3 + Return of year 4 + Return on year 5} ÷ Number of years
= {5.0% + 14.0% + 11.0% - 8.0% + 6.0%} ÷ 5
= 28.0% ÷ 5
= 5.60%
Variance is computed using the equation given below:
Variance = {(Return of year 1 - AR) 2 + (Return of year 2 - AR) 2 + (Return of year 3 - AR) 2 + (Return of year 4 - AR) 2} ÷ {Number of years - 1}
= {(5.0% - 5.60%) 2 + (14.0% - 5.60%) 2 + {11.0% - 5.60%) 2 + (-8.0% - 5.60%) 2} + {6.0% - 5.60%) 2 ÷ {5 - 1}
= {(-0.6%) 2 + (8.40%) 2 + (5.4%) 2 + (-13.60%) 2 + (0.40%) 2} ÷ 4
= {0.000036 + 0.007056 + 0.002916 + 0.018496 + 0.000016} ÷ 4
= 0.02852 ÷ 4
= 0.00713 or 71.3%
Standard deviation is computed using the equation given below:
Standard deviation = (Variance) ½
= (71.3%) ½
= 8.444%
Hence, the standard deviation is 8.444%
