Question

a) Calculate the expected return andstandard deviation of a portfolio invested in the following two risky assets.

 Security W E(r) σ A 40% 10 18.63 B 60% 5 8.27

Correlation coefficient ρ= - 0.49

b) Calculate the expected return of a complete portfolio invested equally in the risky portfolio calculated previously (a) and risk-free asset with 4% return. Compare your results?

 a) Security Weight E( R) Standard Deviation A 40% 10% 18.63 B 60% 5% 8.27 Correlation coefficient ρ -0.49 Expected Portfolio Return E(P) 7.00% W(A)* ER(A) +W(B)*ER(B) [40%*10%+60%*5%] Variance of Portfolio =Standard Deviation of Portfolio ^2 ----->SD(P)^2 W(A)^2 *SD(A) ^2+ W(B)^2 *SD(B)^2 +2*W(A)*W(B)*SD(A)*SD(B)*ρ 43.91646048 Standard Deviation of Portfolio 6.626949561 b) Retrun Weight Risk-free asset (Rf) 4% 50% Expected Portfolio Return 7.00% 50% Expected Return 5.500% W(Rf)* ER(Rf) +W(P)*ER(P) [4%*50%+ 7%*50%] The retun has dropped to 5.5% for complete portfolio invested equally in the risky portfolio calculated previously (a) and risk-free asset with 4% return

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