Based on the following information, calculate the exzpected return and standard

Question

Based on the following information, calculate the exzpected return and standard deviation for the two stocks:

Calculatin Returns and Standard Deviations                               Rate of Return if State Occurs

State of Economy       Probability of State Economy                           Stock (A)      Stock (B)

Recession                                       .15                                                  .05              - .17

Normal                                         .65                                                   .08                .12

Boom                                           .20                                                   .13               .29

Explanation / Answer

Answer The expected return of an asset is the sum of the probability of each return occurring times the probability of that return occurring. So, the expected return of each stock is: E(RA) = 0.15(5.0%) + 0.12(65%) + 0.29(20.0%) = 14.35 % E(RB) = 0.15(-17.0%) + 0.12(8.0%) + 0.29(13.0%) = 2.18 % To calculate the standard deviation, we first need to calculate the variance. Variance sA^2 = [0.15(0.05 – 0.1435)^2 + 0.12(0.65 – 0.1435)^2 + 0.29(0.20 – 0.1435)^2] = 0.03302 Standard deviation sA = 0.18172 =18.17% Variance sB^2 = [0.15(-0.17 – .0218)^2 + 0.12(0.08– 0.0218)^2 + 0.29(0.13 – 0.0218)^2] = 0.0093196 Standard deviation sV =0 .09654 = 9.65 % the expected return and standard deviation for Stock A are 14.35 and 18.17 respectively The expected return and standard deviation for Stock B are 2.18and 9.65 respectively

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