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%