Consider the following information: Rate of Return If State Occurs State of Prob

Question

Consider the following information: Rate of Return If State Occurs State of Probability of Economy State of Economy Stock A Stock B Stock C Boom .15 .39 .49 .29 Good .55 .15 .20 .08 Poor .25 .01 .09 .07 Bust .05 .20 .24 .10 a. Your portfolio is invested 24 percent each in A and C, and 52 percent in B. What is the expected return of the portfolio? (Do not round intermediate calculaitons. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Expected return % b-1 What is the variance of this portfolio? (Do not round intermediate calculations and round your answer to 5 decimal places, e.g., 32.16161.) Variance b-2 What is the standard deviation? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Standard deviation %

Explanation / Answer

Stock A Scenario Probability Return =rate of return * probability Actual return -expected return(A) (A)^2* probability Boom 0.15 39 5.85 26.15 102.573375 Good 0.55 15 8.25 2.15 2.542375 Poor 0.25 -1 -0.25 -13.85 47.955625 Bust 0.05 -20 -1 -32.85 53.956125 Expected return = sum of weighted return = 12.85 Sum= 207.0275 Standard deviation= Standard deviation of stock A =(sum)^(1/2) 14.38845023 Stock B Scenario Probability Return =rate of return * probability Actual return -expected return(B) (B)^2* probability Boom 0.15 49 7.35 34.1 174.4215 Good 0.55 20 11 5.1 14.3055 Poor 0.25 -9 -2.25 -23.9 142.8025 Bust 0.05 -24 -1.2 -38.9 75.6605 Expected return = sum of weighted return = 14.90 Sum= 407.19 Standard deviation= Standard deviation of stock B =(sum)^(1/2) 20.17894943 Stock C Scenario Probability Return =rate of return * probability Actual return -expected return(C) (C)^2* probability Boom 0.15 29 4.35 14.1 29.8215 Good 0.55 8 4.4 -6.9 26.1855 Poor 0.25 -7 -1.75 -21.9 119.9025 Bust 0.05 -27 -1.35 -41.9 87.7805 Expected return = sum of weighted return = 5.65 Sum= 263.69 Standard deviation= Standard deviation of stock C =(sum)^(1/2) 16.23853442 Covariance: A and B Probability Actual return -expected return(A) Actual return -expected return(B) (A)*(B)*probability Boom 0.15 26.15 34.1 133.75725 Good 0.55 2.15 5.1 6.03075 Poor 0.25 -13.85 -23.9 82.75375 Bust 0.05 -32.85 -38.9 63.89325 Covariance=sum= 286.435 CorrelationAB= Covariance/(std devA*std devB)= 0.99 Covariance: A and C Probability Actual return -expected return(A) Actual return -expected return(C) (A)*(C)*probability Boom 0.15 26.15 14.1 55.30725 Good 0.55 2.15 -6.9 -8.15925 Poor 0.25 -13.85 -21.9 75.82875 Bust 0.05 -32.85 -41.9 68.82075 Covariance=sum= 191.7975 CorrelationAC= Covariance/(std devA*std devC)= 0.820884571 Covariance: B and C Probability Actual return -expected return(B) Actual return -expected return(C) (A)*(B)*probability Boom 0.15 34.1 14.1 72.1215 Good 0.55 5.1 -6.9 -19.3545 Poor 0.25 -23.9 -21.9 130.8525 Bust 0.05 -38.9 -41.9 81.4955 Covariance=sum= 265.115 Correlation= Covariance/(std devB*std devC)= 0.809075254 weight in portfolio stock A 0.24 Stock B 0.52 Stock C 0.24 Expected return= 12.19 weight in portfolio stock A 0.24 Stock B 0.52 Stock C 0.24 Variance= 0.02970 Standard deviation 17.23

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