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Refer to the table below. 3 Doors, Inc. Down Co. Expected return, E (R) 14 %...

Refer to the table below. 3 Doors, Inc. Down Co. Expected return, E (R) 14 % 7.5 % Standard deviation, σ 26 17 Correlation .38 Using the information provided on the two stocks in the table above, find the expected return and standard deviation on the minimum variance portfolio. (Round your answer to 2 decimal places. Omit the "%" sign in your response.) Expected return % Standard deviation %

Solutions

Expert Solution

To find the fraction of wealth to invest in 3 Doors that will result in the risky portfolio with minimum variance the following formula to determine the weight of 3 Doors in risky portfolio should be used

Where
3 Doors E[R(d)]= 14.00%
Down co E[R(e)]= 7.50%
3 Doors Stdev[R(d)]= 26.00%
Down co Stdev[R(e)]= 17.00%
Var[R(d)]= 0.06760
Var[R(e)]= 0.02890
T bill Rf= 12.00%
Correl Corr(Re,Rd)= 0.38
Covar Cov(Re,Rd)= 0.0168
3 Doors Therefore W(*d)= 0.1924
Down co W(*e)=(1-W(*d))= 0.8076
Expected return of risky portfolio= 8.75%
Risky portfolio std dev= 16.30%
Where
Var = std dev^2
Covariance = Correlation* Std dev (r)*Std dev (d)
Expected return of the risky portfolio = E[R(d)]*W(*d)+E[R(e)]*W(*e)
Risky portfolio standard deviation =( w2A*σ2(RA)+w2B*σ2(RB)+2*(wA)*(wB)*Cor(RA,RB)*σ(RA)*σ(RB))^0.5

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