Question

An investor can design a risky portfolio based on two stocks, A and B. Stock A has an expected return of 16% and a standard deviation of return of 30%. Stock B has an expected return of 11% and a standard deviation of return of 15%. The correlation coefficient between the returns of A and B is .5. The risk-free rate of return is 5%. The proportion of the optimal risky portfolio that should be invested in stock B is approximately

Answer #1

Weight of A= {(Expected return of A- risk free rate)*(SD of B)^2}-{(Expected return of B- risk free rate)*SD of A*(corr of A&B} divided by

{(Expected return of A- risk free rate)*(SD of B)^2}+{(Expected return of B- risk free rate)*SD of A* Corr of A&B}-{(Expected return of A- risk free rate)+(Expected return of B- risk free rate)}*SD of A* SD of B*(Corr of A&B)}

={{(0.16-0.05)*(0.15^2)}-{(0.11-0.05)*0.5*0.30}}/{(0.16-0.05)*(0.15^2)+((0.11-0.05)*(0.30^2)-{(0.16-0.05+0.11-0.05)*}0.5

=(0.0025-0.0090)/(0.0025+0.0054-0.00382)

=-0.0065/0.00405.

since weight of A is coming negative we will consider it 0.

Weight of B = 1- Weight of A= 100%

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