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Find portfolio variance You invest $6,000 in the stock and $4,000 in the bond outcome P Rs Rb recession 30% -11% 16% normal 40% 13% 6% boom 30% 27% -4%

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Finance

Find portfolio variance You invest $6,000 in the stock and$4,000 in the bond

outcomePRsRb
recession30%-11%16%
normal40%13%6%
boom30%27%-4%

Answer & Explanation Solved by verified expert
4.4 Ratings (944 Votes)

Stock
Scenario Probability Return% =rate of return% * probability Actual return -expected return(A)%
Recession 0.3 -11 -3.3 -21
Normal 0.4 13 5.2 3
Boom 0.3 27 8.1 17
Expected return %= sum of weighted return = 10 Sum=Variance Stock=
Standard deviation of Stock% =(Variance)^(1/2)
Bond
Scenario Probability Return% =rate of return% * probability Actual return -expected return(A)%
Recession 0.3 16 4.8 10
Normal 0.4 6 2.4 0
Boom 0.3 -4 -1.2 -10
Expected return %= sum of weighted return = 6 Sum=Variance Bond=
Standard deviation of Bond% =(Variance)^(1/2)
Covariance Stock Bond:
Scenario Probability Actual return% -expected return% for A(A) Actual return% -expected return% For B(B) (A)*(B)*probability
Recession 0.3 -21 10 -0.0063
Normal 0.4 3 0 0
Boom 0.3 17 -10 -0.0051
Covariance=sum= -0.0114
Correlation A&B= Covariance/(std devA*std devB)= -0.98643085
Expected return%= Wt Stock*Return Stock+Wt Bond*Return Bond
Expected return%= 0.6*10+0.4*6
Expected return%= 8.4
Variance =( w2A*?2(RA) + w2B*?2(RB) + 2*(wA)*(wB)*Cor(RA, RB)*?(RA)*?(RB))
Variance =0.6^2*0.1492^2+0.4^2*0.07746^2+2*0.6*0.4*0.1492*0.07746*-0.98643
Variance 0.0035

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Transcribed Image Text

Find portfolio variance You invest $6,000 in the stock and$4,000 in the bondoutcomePRsRbrecession30%-11%16%normal40%13%6%boom30%27%-4%

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