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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