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What is the variance of the returns on a portfolio that is invested 40 percent in...

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Finance

What is the variance of the returns on a portfolio that isinvested 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

.00091

.00136

.00107

.00118

Please show work

Answer & Explanation Solved by verified expert
4.3 Ratings (938 Votes)

Stock S
Scenario Probability Return% =rate of return% * probability Actual return -expected return(A)% (A)^2* probability
Boom 0.06 22 1.32 7.4 0.00032856
Normal 0.92 15 13.8 0.4 1.472E-05
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
Boom 0.06 18 1.08 3.86 8.93976E-05
Normal 0.92 14 12.88 -0.14 1.8032E-06
Bust 0.02 9 0.18 -5.14 5.28392E-05
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
Boom 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
Variance =( w2A*?2(RA) + w2B*?2(RB) + 2*(wA)*(wB)*Cor(RA, RB)*?(RA)*?(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 0.00091

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Transcribed Image Text

What is the variance of the returns on a portfolio that isinvested 40 percent in Stock S and 60 percent in Stock T?State ofEconomyProbability ofState of EconomyRate of Returnif State OccursStock SStock TBoom.06.22.18Normal.92.15.14Bust.02?.26.09.00091.00136.00107.00118Please show work

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