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

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05-02-2021
Business

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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

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Adnansoomro2019idn Adnansoomro2019idn · Answer 1 · 2021-02-07T22:55:12-05:00

Answer:

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:

= [tex]\frac{(w_{a} - RFR )SDB^{2} - (w_{b} - RFR )SDA*SDB*CC }{(w_{a} - RFR )SDB^{2} + (w_{b} - RFR )SDA^{2} * (w_{a} -RFR + w_{b} -RFR )SDA*SDB*CC }[/tex]

Where,

[tex]w_{a}[/tex] = Expected Return of Stock A = 18%

[tex]w_{b}[/tex] = 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.

= [tex]\frac{(18 - 12 )3^{2} - (14 - 12 )18*3*0.50 }{(18 - 12 )3^{2} + (14 - 12 )18^{2} * (18 -12 + 14 -12 )18*3*0.50 }[/tex]

= [tex]\frac{0}{486}[/tex]

= 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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