Question

An investor can design a risky portfolio based on two stocks, A and B. Stock A has an expected return of 21% and a standard deviation of return of 35%. Stock B has an expected return of 14% and a standard deviation of return of 21%. The correlation coefficient between the returns of A and B is 0.3. The risk-free rate of return is 1.9%. What is the expected return on the optimal risky portfolio?

Answer #1

For optimally risky portfolio we should using following
formula

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 )))

Weight of A =((21%-1.9%)*21%^{2}
-(14%-1.9%)*35%*21%*0.3)/((21%-1.9%)*21%^{2} +
(14%-1.9%)*35%^{2} - ((21%-1.9%) +(14%-1.9%) *35%*21%*0.3)
= 0.3516

Weight of B = 1- 0.3516 = 0.6486

Expected Return of optimally risky portfolio =
0.3516*21%+0.6486*14% = 16.46%

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