Your portfolio is invested 30 percent each in A and C and 40 percent in B. What

Question

Your portfolio is invested 30 percent each in A and C and 40 percent in B. What is the expected return of the portfolio? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)

What is the variance of this portfolio? (Do not round intermediate calculations. Round your answer to 5 decimal places (e.g., 32.16161).)

What is the standard deviation of this portfolio? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)

Consider the following information:

Explanation / Answer

Where

portfolio return =   sum(product of constituent weight*costituent expected return)

=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)

standard deviation = (variance)^(1/2)

Stock A Scenario Probability Return =rate of return * probability Actual return -expected return(A) (A)^2* probability Boom 0.15 0.35 0.0525 0.2455 0.009040538 Good 0.45 0.12 0.054 0.0155 0.000108113 Poor 0.35 0.01 0.0035 -0.0945 0.003125588 Bust 0.05 -0.11 -0.0055 -0.2145 0.002300513 Expected return = sum of weighted return = 0.1045 Sum= 0.01457475 Standard deviation= Standard deviation of stock A =(sum)^(1/2) 0.120725929 Stock B Scenario Probability Return =rate of return * probability Actual return -expected return(B) (B)^2* probability Boom 0.15 0.45 0.0675 0.343 0.01764735 Good 0.45 0.1 0.045 -0.007 2.205E-05 Poor 0.35 0.02 0.007 -0.087 0.00264915 Bust 0.05 -0.25 -0.0125 -0.357 0.00637245 Expected return = sum of weighted return = 0.11 Sum= 0.026691 Standard deviation= Standard deviation of stock B =(sum)^(1/2) 0.163373805 Stock C Scenario Probability Return =rate of return * probability Actual return -expected return(C) (C)^2* probability Boom 0.15 0.33 0.0495 0.223 0.00745935 Good 0.45 0.17 0.0765 0.063 0.00178605 Poor 0.35 -0.05 -0.0175 -0.157 0.00862715 Bust 0.05 -0.09 -0.0045 -0.197 0.00194045 Expected return = sum of weighted return = 0.104 Sum= 0.019813 Standard deviation= Standard deviation of stock C =(sum)^(1/2) 0.140758659 Covariance: A and B Probability Actual return -expected return(A) Actual return -expected return(B) (A)*(B)*probability Boom 0.15 0.2455 0.343 0.012630975 Good 0.45 0.0155 -0.007 -4.8825E-05 Poor 0.35 -0.0945 -0.087 0.002877525 Bust 0.05 -0.2145 -0.357 0.003828825 Covariance=sum= 0.0192885 CorrelationAB= Covariance/(std devA*std devB)= 0.98 Covariance: A and C Probability Actual return -expected return(A) Actual return -expected return(C) (A)*(C)*probability Boom 0.15 0.2455 0.223 0.008211975 Good 0.45 0.0155 0.063 0.000439425 Poor 0.35 -0.0945 -0.157 0.005192775 Bust 0.05 -0.2145 -0.197 0.002112825 Covariance=sum= 0.015957 CorrelationAC= Covariance/(std devA*std devC)= 0.93902157 Covariance: B and C Probability Actual return -expected return(B) Actual return -expected return(C) (A)*(B)*probability Boom 0.15 0.343 0.223 0.01147335 Good 0.45 -0.007 0.063 -0.00019845 Poor 0.35 -0.087 -0.157 0.00478065 Bust 0.05 -0.357 -0.197 0.00351645 Covariance=sum= 0.019572 Correlation= Covariance/(std devB*std devC)= 0.851094266 weight in portfolio stock A 0.3 Stock B 0.4 Stock C 0.3 Expected return= 10.54% weight in portfolio stock A 0.3 Stock B 0.4 Stock C 0.3 Variance= 0.019564 Standard deviation 13.99%

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