Consider the following information: Rate of Return If State Occurs. Probability

Question

Consider the following information: Rate of Return If State Occurs. Probability of state of economy, Boom=.64, Bust= .36 Stock A, Boom=.11 Bust=.18 Stock C, Boom=.38, Bust=-.04

a. What is the expected return on an equally weighted portfolio of these three stocks? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Expected return 17.58 %

b. 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

A is correct I am just not sure how to find the variance in part B.

Explanation / Answer

Where

variance =

=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 0.64 0.11 0.0704 -0.0252 0.000406426 Bust 0.36 0.18 0.0648 0.0448 0.000722534 Expected return = sum of weighted return = 0.1352 Sum= 0.00112896 Standard deviation= Standard deviation of stock A =(sum)^(1/2) 0.0336 Stock B Scenario Probability Return =rate of return * probability Actual return -expected return(B) (B)^2* probability Boom 0.64 0.2 0.128 0.036 0.00082944 Bust 0.36 0.1 0.036 -0.064 0.00147456 Expected return = sum of weighted return = 0.164 Sum= 0.002304 Standard deviation= Standard deviation of stock B =(sum)^(1/2) 0.048 Stock C Scenario Probability Return =rate of return * probability Actual return -expected return(C) (C)^2* probability Boom 0.64 0.38 0.2432 0.216 0.02985984 Bust 0.36 -0.04 -0.0144 -0.204 0.01498176 Expected return = sum of weighted return = 0.2288 Sum= 0.0448416 Standard deviation= Standard deviation of stock C =(sum)^(1/2) 0.211758353 Covariance: A and B Probability Actual return -expected return(A) Actual return -expected return(B) (A)*(B)*probability Boom 0.64 -0.0252 0.036 -0.000580608 Bust 0.36 0.0448 -0.064 -0.001032192 Covariance=sum= -0.0016128 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 0.64 -0.0252 0.216 -0.003483648 Bust 0.36 0.0448 -0.204 -0.003290112 Covariance=sum= -0.00677376 CorrelationAC= Covariance/(std devA*std devC)= -0.952028561 Covariance: B and C Probability Actual return -expected return(B) Actual return -expected return(C) (A)*(B)*probability Boom 0.64 0.036 0.216 0.00497664 Bust 0.36 -0.064 -0.204 0.00470016 Covariance=sum= 0.0096768 Correlation= Covariance/(std devB*std devC)= 0.952028561 weight in portfolio stock A 0.333333333 Stock B 0.333333333 Stock C 0.333333333 Expected return= 17.60% weight in portfolio stock A 0.2 Stock B 0.2 Stock C 0.6 Variance= 0.016887

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