Couldn\'t get the Variance right.....HELP!! Consider the following information:

Question

Couldn't get the Variance right.....HELP!!

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 0.58 0.07 0.15 0.33 Bust 0.42 0.16 0.06 - 0.06. What is the expected return on an equally weighted portfolio of these three stocks? (Do not round intermediate calculations and round your final answer to 2 decimal places, (e.g., 32.16))Expected return 12.87 % What is the variance of a portfolio invested 20 percent each in A and B and 60 percent in C? (Do not round intermediate calculations and round your answer to 6 decimal places, (e.g., 32.161616)) Variance

Explanation / Answer

Variance is calculated as

=w2A*2(RA) + w2B*2(RB) + w2C*2(RC)+ 2*(wA)*(wB)*Cor(RA, RB)*(RA)*(RB) + 2*(wA)*(wC)*Cor(RA, RC)*(RA)*(RC) + 2*(wC)*(wB)*Cor(RC, RB)*(RC)*(RB)

Stock A Scenario Probability Return =rate of return * probability Actual return -expected return(A) (A)^2* probability Boom 0.58 0.07 0.0406 -0.0378 0.000829 Bust 0.42 0.16 0.0672 0.0522 0.001144 Expected return = sum of weighted return = 0.1078 Sum(Variance)= 0.001973 Standard deviation= Standard deviation of stock A =(sum)^(1/2) 0.04442 Stock B Scenario Probability Return =rate of return * probability Actual return -expected return(B) (B)^2* probability Boom 0.58 0.15 0.087 0.0378 0.000829 Bust 0.42 0.06 0.0252 -0.0522 0.001144 Expected return = sum of weighted return = 0.1122 Sum= 0.001973 Standard deviation= Standard deviation of stock B =(sum)^(1/2) 0.04442 Stock C Scenario Probability Return =rate of return * probability Actual return -expected return(C) (C)^2* probability Boom 0.58 0.33 0.1914 0.2178 0.027513 Bust 0.42 -0.06 -0.0252 -0.1722 0.012454 Expected return = sum of weighted return = 0.1662 Sum= 0.039968 Standard deviation= Standard deviation of stock C =(sum)^(1/2) 0.199919 Covariance: A and B Probability Actual return -expected return(A) Actual return -expected return(B) (A)*(B)*probability Boom 0.58 -0.0378 0.0378 -0.00083 Bust 0.42 0.0522 -0.0522 -0.00114 Covariance=sum= -0.00197 CorrelationAB= Covariance/(std devA*std devB)= -1.00 Covariance: A and C Probability Actual return -expected return(A) Actual return -expected return(C) (A)*(C)*probability Boom 0.58 -0.0378 0.2178 -0.00478 Bust 0.42 0.0522 -0.1722 -0.00378 Covariance=sum= -0.00855 CorrelationAC= Covariance/(std devA*std devC)= -0.96283 Covariance: B and C Probability Actual return -expected return(B) Actual return -expected return(C) (A)*(B)*probability Boom 0.58 0.0378 0.2178 0.004775 Bust 0.42 -0.0522 -0.1722 0.003775 Covariance=sum= 0.00855 Correlation= Covariance/(std devB*std devC)= 0.96283 weight in portfolio stock A 0.333 Stock B 0.3333 Stock C 0.333333 Expected return of portfolio= 0.128694 weight in portfolio stock A 0.2 Stock B 0.2 Stock C 0.6 Variance= 0.014388

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