A project has a 0.88 chance of doubling your investment in a year and a 0.12 chance of halving your investment in a year. What is the standard deviation of the rate of return on this investment?

Probability         Value

0.48                    $2 00

0.52                    $50

Expected value or E(x) = probability * ( value)  

Expected value or E(x) = 0.88*200 + 0.12*50 = $182

Variance of (x) = E(x^2) - (E(x))^2

= (0.88 * 200^2 + 0.12 * 50^2) - (182)^2

= (35,200 + 300) - 33124

= 35500-33124

= 2376

Standard deviation = sqrt (variance)

= sqrt(2376)

= 48.74%

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