8-1: A stocks returns have the following distribution: Demand for the Company\'s

Question

8-1: A stocks returns have the following distribution: Demand for the Company'sProducts     Probability of This DemandOccuring   Return of demand if this demandoccurs Weak                                                                     0.1                                                                     (50%) Belowaverage                                                   0.2                                                                          (5) Average                                                            0.4                                                                                 16 AboveAverage                                                0.2                                                                                25 Strong                                                                  0.1                                                                                60                                                                              1.0 Calculate the stocks expected return, standard deviation andcoefficient of variation. 8-1: A stocks returns have the following distribution: Demand for the Company'sProducts     Probability of This DemandOccuring   Return of demand if this demandoccurs Weak                                                                     0.1                                                                     (50%) Belowaverage                                                   0.2                                                                          (5) Average                                                            0.4                                                                                 16 AboveAverage                                                0.2                                                                                25 Strong                                                                  0.1                                                                                60                                                                              1.0 Calculate the stocks expected return, standard deviation andcoefficient of variation. Calculate the stocks expected return, standard deviation andcoefficient of variation.

Explanation / Answer

Calculating Expected Return E(R): Expected Return E(R ) = (0.10* -0.50) + (0.20 * -0.05) + (0.40 * 0.16) + (0.20 * 0.25) +(0.10 * 0.60) Expected Return E(R ) = -0.05 +(-0.01) + 0.064 + 0.05 + 0.06 Expected Return E(R ) =   -0.06+ 0.174 Expected Return E(R ) = 0.114(or) 11.40% Calculating Standard Deviation(2): Standard Deviation(2) = [0.10 * (-0.50 -0.114)2 + 0.20 (-0.05 - 0.114)2 + 0.40 *(0.16 - 0.114)2 + 0.20 (0.25 - 0.114)2 + 0.10* (0.60 - 0.114)2] Standard Deviation(2) = [(0.10 * 0.376996) + (0.20 *0.026896) + (0.40 * 0.075076) + (0.20 * 0.132496) + (0.10 *0.509796)] Standard Deviation(2) = [0.0376996 + 0.005379 + 0.030030 +0.026499 + 0.050979] Standard Deviation(2) = 0.1505866 Standard Deviation ()  =0.1505866 Standard Deviation ()  = 0.3880 (or) 38.80% Calculating Expected Return E(R): Expected Return E(R ) = (0.10* -0.50) + (0.20 * -0.05) + (0.40 * 0.16) + (0.20 * 0.25) +(0.10 * 0.60) Expected Return E(R ) = -0.05 +(-0.01) + 0.064 + 0.05 + 0.06 Expected Return E(R ) =   -0.06+ 0.174 Expected Return E(R ) = 0.114(or) 11.40% Calculating Standard Deviation(2): Standard Deviation(2) = [0.10 * (-0.50 -0.114)2 + 0.20 (-0.05 - 0.114)2 + 0.40 *(0.16 - 0.114)2 + 0.20 (0.25 - 0.114)2 + 0.10* (0.60 - 0.114)2] Standard Deviation(2) = [(0.10 * 0.376996) + (0.20 *0.026896) + (0.40 * 0.075076) + (0.20 * 0.132496) + (0.10 *0.509796)] Standard Deviation(2) = [0.0376996 + 0.005379 + 0.030030 +0.026499 + 0.050979] Standard Deviation(2) = 0.1505866 Standard Deviation ()  =0.1505866 Standard Deviation ()  = 0.3880 (or) 38.80%
Hope it may help you Calculating Expected Return E(R): Expected Return E(R ) = (0.10* -0.50) + (0.20 * -0.05) + (0.40 * 0.16) + (0.20 * 0.25) +(0.10 * 0.60) Expected Return E(R ) = -0.05 +(-0.01) + 0.064 + 0.05 + 0.06 Expected Return E(R ) =   -0.06+ 0.174 Expected Return E(R ) = 0.114(or) 11.40% Calculating Standard Deviation(2): Standard Deviation(2) = [0.10 * (-0.50 -0.114)2 + 0.20 (-0.05 - 0.114)2 + 0.40 *(0.16 - 0.114)2 + 0.20 (0.25 - 0.114)2 + 0.10* (0.60 - 0.114)2] Standard Deviation(2) = [(0.10 * 0.376996) + (0.20 *0.026896) + (0.40 * 0.075076) + (0.20 * 0.132496) + (0.10 *0.509796)] Standard Deviation(2) = [0.0376996 + 0.005379 + 0.030030 +0.026499 + 0.050979] Standard Deviation(2) = 0.1505866 Standard Deviation ()  =0.1505866 Standard Deviation ()  = 0.3880 (or) 38.80%

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