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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