Rate of Return If State Occurs State of Probability of Economy State of Economy

Question

Rate of Return If State Occurs State of Probability of Economy State of Economy Stock A Stock B Recession .17 .05 .21 Normal .62 .09 .08 Boom .21 .16 .25

Calculate the expected return for each stock. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

Expected return Stock A % Stock B %

Calculate the standard deviation for each stock. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

Standard deviation Stock A % Stock B %

Explanation / Answer

  State of Economy Probability Return-Stock A Prob.*Return (Return-Expected Return0.0979) (Return-Expected Return0.0979)^2*Prob.   Recession 0.17 0.05 0.0085 -0.0479 0.00039   Normal 0.62 0.09 0.0558 -0.0079 3.87E-05   Boom 0.21 0.16 0.0336 0.0621 0.00081 Sum 0.0979 Variance 0.001239 Std.Devn.= SQ.rt.of variance= 0.035194 3.52% Expected Return(A)=(0.05*0.17)+(0.09*0.62)+(0.16*0.21)= 9.79% Std.Devn.(A)= SQ.rt.of variance= 3.52%   State of Economy Probability Return-Stock B Prob.*Return (Return-Expected Return0.0664) (Return-Expected Return0.0979)^2*Prob.   Recession 0.17 -0.21 -0.0357 -0.2764 0.012987   Normal 0.62 0.08 0.0496 0.0136 0.000115   Boom 0.21 0.25 0.0525 0.1836 0.007079 0.0664 Variance 0.020181 Std.Devn.= SQ.rt.of variance= 0.14206 14.21% Expected Return(B)=(-0.21*0.17)+(0.08*0.62)+(0.25*0.21)= 6.64% Std.Devn.(B)= SQ.rt.of variance= 14.21% Expected Return(A) 9.79% Expected Return(B) 6.64% Std.Devn.(A) 3.52% Std.Devn.(B) 14.21%

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