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In-line exercise: mean return and volatility, solution (2)

In four years, a portfolio of common stocks realized returns of 40%, 0%, -30%, and 10%. Compute the (arithmetic) mean, variance, and standard deviation of returns. For this exercise, divide by the number of returns (not one less) to compute the variance


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mean = (1/4)(0.4 + 0.0 + (-0.3) + 0.1) = (1/4)(.2) = 0.05 or 5%

variance = (1/4)((0.4-0.05)^2 + (0.0-0.05)^2 + (-0.3-0.05)^2 + (0.1-0.05)^2) = (1/4)(0.25) = 0.0625

standard deviation = sqrt(0.0625) = 0.25 or 25%


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Phil Dybvig
Finally, the standard deviation is just the square root of the variance.

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