Question

# Consider two risky securities A and B. A has an expected rate of return of 15%...

Consider two risky securities A and B. A has an expected rate of return of 15% and a standard deviation of 20%. B has an expected rate of return of 10% and a standard deviation of 16%. The correlation coefficient of A and B is 0.2. Risk-free rate is 6%. The weights of A and B in the optimal risky portfolio are _____ and _____, respectively.

 A. 0.67; 0.33 B. 0.52; 0.48 C. 0.54; 0.46 D. 0.64; 0.36 E. 0.43; 0.57

Weight of A = ((Return of A - Risk Free Rate) * (Standard Deviation B)2 - (Return of B - Risk Free Rate)*(Standard Deviation A* Standard Deviation B*Correlation Coefficient ))/((Return of A - Risk Free Rate) * (Standard Deviation B)2 +(Return of B - Risk Free Rate) * (Standard Deviation A)2 - ((Return of A - Risk Free Rate) +(Return of B - Risk Free Rate))*(Standard Deviation A* Standard Deviation B*Correlation Coefficient )))
=​​​​​​((15%-6%)*16%^2-(10%-6%)*20%*16%*0.2)/(((15%-6%)*16%^2+(10%-6%)*20%^2-((15%-6%+10%-6%)*20%*16%*0.2))=66.67% or 0.67

Weight of B =1-0.67 =0.33 (Option a is correct option)

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