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Question 6 What is the variance of the returns on a portfolio that is invested 40...

Question 6

  1. What is the variance of the returns on a portfolio that is invested 40 percent in Stock S and 60 percent in Stock T?

    State of

    Economy

    Probability of

    State of Economy

    Rate of Return

    if State Occurs

    Stock S

    Stock T

    Boom

    .06

    .22

    .18

    Normal

    .92

    .15

    .14

    Bust

    .02

    −.26

    .09

Solutions

Expert Solution

Stock S
Scenario Probability Return% =rate of return% * probability Actual return -expected return(A)% (A)^2* probability
Bad 0.06 22 1.32 7.4 0.00032856
Normal 0.92 15 13.8 0.4 0.0000147200
Bust 0.02 -26 -0.52 -40.6 0.00329672
Expected return %= sum of weighted return = 14.6 Sum=Variance Stock S= 0.00364
Standard deviation of Stock S% =(Variance)^(1/2) 6.03
Stock T
Scenario Probability Return% =rate of return% * probability Actual return -expected return(A)% (B)^2* probability
Bad 0.06 18 1.08 3.86 0.0000893976
Normal 0.92 14 12.88 -0.14 0.0000018032
Bust 0.02 9 0.18 -5.14 0.0000528392
Expected return %= sum of weighted return = 14.14 Sum=Variance Stock T= 0.00014
Standard deviation of Stock T% =(Variance)^(1/2) 1.2
Covariance Stock S Stock T:
Scenario Probability Actual return% -expected return% for A(A) Actual return% -expected return% For B(B) (A)*(B)*probability
Bad 0.06 7.4 3.86 0.000171384
Normal 0.92 0.4 -0.14 -0.000005152
Bust 0.02 -40.6 -5.14 0.000417368
Covariance=sum= 0.0005836
Correlation A&B= Covariance/(std devA*std devB)= 0.805977717
Expected return%= Wt Stock S*Return Stock S+Wt Stock T*Return Stock T
Expected return%= 0.4*14.6+0.6*14.14
Expected return%= 14.32
Variance =( w2A*σ2(RA) + w2B*σ2(RB) + 2*(wA)*(wB)*Cor(RA, RB)*σ(RA)*σ(RB))
Variance =0.4^2*0.06033^2+0.6^2*0.012^2+2*0.4*0.6*0.06033*0.012*0.80598
Variance 0.00091000

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