1) An investor can design a risky portfolio based on two stocks, A and B. Stock A has an expected return of "18%" and a standard deviation of return of 18.0%. Stock B has an expected return of 14% and a standard deviation of return of 3%. The correlation coefficient between the returns of A and B is 0.50. The risk-free rate of return is 12%. The proportion of the optimal risky portfolio that should be invested in stock A is

So, the proportion of the optimal risky portfolio that should be invested in Stock A is 0% because the weight of Stock A is 0.

Explanation:

Solution:

Data Given:

Stock A = Expected Return 18%

Standard Deviation = 18.0%

Stock B = Expected Return 14%

Standard Deviation = 3%

Correlation Coefficient for Stock A and B = 0.50

Risk Free rate of return = 12%

For Proportion of the optimal risky portfolio that should be invested in Stock A can be computed through the calculation of weight of Stock A in optimal portfolio as follows:

=

Where,

= Expected Return of Stock A = 18%

= Expected Return of Stock B = 14%

SDA = Standard Deviation of Stock A = 18%

SDB = Standard Deviation of Stock B = 3%

CC = Correlation Coefficient = 0.50

Plugging in the values, we will get.

=

=

= 0

So, the proportion of the optimal risky portfolio that should be invested in Stock A is 0% because the weight of Stock A is 0.

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