Question

A project will double your investment in one year with probability .5, otherwise you'll lose half your investment. What is the standard deviation of this investment?

Answer 1

Expected return = (P1 * R1) + (P2 * R2)

P1 = Probability of doubling the investment = 0.5
P2 = Probability of lose half of your investment = 1 - 0.5 = 0.5
If the investment get doubled, the the return (R1) = 100%
If the investment lose half of your investment, then the raturn (R2) = -50%

Expected return = (0.5 * 100%) + (0.5 * (-50%))
= 50% - 25%
= 25%

Standard deviation = (p1*(R1-E[R])^2 + p2*(R2-E[R])^2)^(1/2)
= (0.5 * (100% - 25%)^2 + 0.5 * (-50 - 25%)^2)^(1/2)
= (0.28125 + 0.28125)^(1/2)
= 0.5625^(1/2)
= 0.75 or 75%

Standard deviation = 0.75 or 75%

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