The probability of the economy booming is 10 percent, while it is 60 percent for being normal, and 30 percent for being recessionary. A stock is expected to return 16 percent in a boom, 11 percent in a normal economy, and lose 8 percent in a recession. What is the standard deviation of the returns?

9.15%

Explanation:

Expected return = Respective return * Respective probability

Expected return = (0.1*16) + (0.6*11) + (0.3*-8)

Expected return = 5.8%

Probability        Return        Probability*(Return-Expected Return)^2

0.1                         16                   [0.1*(16-5.8)^2] = 10.404

0.6                        11                    [0.6*(11-5.8)^2] = 16.224

0.3                       -8                     [0.3*(-8-5.8)^2] = 57.132

                            Total =                                         83.76%

Standard deviation = [Total probability*(Return-Expected Return)^2/Total probability]^(1/2)

Standard deviation = (83.76)^(1/2)

Standard deviation = 9.15204895092%

Standard deviation = 9.15%

rational decision making is a multi-step process for making choices between alternatives. the process of rational decision making favors logic, objectivity, and analysis over subjectivity and insight. the word “rational” in this context does not mean sane or clear-headed as it does in the colloquial sense.

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