A stock had returns of 19.02 percent, 22.72 percent, −16.16 percent, 9.44 percent, and 28.51 percent...

A stock had returns of 19.02 percent, 22.72 percent, −16.16 percent, 9.44 percent, and 28.51 percent for the past five years. What is the standard deviation of the returns?

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Expert Solution

R₁=19.02%, R₂=22.72%, R₃= -16.16%, R₄=9.44%, R₅=28.51%

To find the standard deviation of returns, first we need to find the Average return over 5 year period

Average return over 5 year period = R_A = (sum of returns of 5 years) / No of years = (R₁ + R₂ + R₃ + R₄ + R₅) / 5

R_A = [19.02% + 22.72% + (-16.16%) + 9.44% + 28.51%] / 5 = [19.02% + 22.72% -16.16% + 9.44% + 28.51%] / 5 = 63.53% / 5 = 12.706%

Let R_i = Return of ith year , n = number of years = 5, then

Variance of returns = 0.12338256 / 5 = 0.024676512

Now,

Standard deviation of returns = 0.1570875 = 15.70875% = 15.71% (rounded to two decimal places)

Hence Standard deviation returns = 15.71%

jeff jeffy answered 8 months ago

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