A manager is attempting to assess the probability of a recession ending in the next six months and its impact on expected profitability.The manager believes there is a 33 percent chance the recession will end in six months and profits will return to $100 million.However,there is a 67 percent chance the recession will not end in six months,resulting in a $7 million loss.The standard deviation of profits over the next six months is:

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The expected profit is calculated as (0.33 * $100 million) + (0.67 * -$7 million) = $28.31 million. The variance is (0.33 * ($100 million - $28.31 million)^2) + (0.67 * (-$7 million - $28.31 million)^2) = $2,531.25 million. The standard deviation is the square root of the variance, which is approximately $50.31 million.

A Manager Is Attempting to Assess the Probability of a Recession