An investor can design a risky portfolio based on two stocks, A and B. StockAhas

Question

An investor can design a risky portfolio based on two stocks, A and B. StockAhas an expected return and a standard deviation of return Stock as an expected return of 14% and a standard d tion of return of 20%. The correlation coefficient between the ofA and B is 0.4. The risk-free rate of return is 5% S. What is the weight of Stock B in the minimum variance portfolio? G 9. What is the proportion of the optimal ri rtfolio that should be invested in stock B? 10. What is the expected return on the optimal risk portfolio? 9 11. What is the standard deviation of the optimal risk portfolio? o 12. What is the reward to volatility ratio of the best feasible CA

Explanation / Answer

Answer:8 The weight of stock B in the minimum variance portfolio:

Weight A =((0.20)2 - (0.20)(0.39)(0.4))/((0.20)2 +(0.39)2- 2 (0.20)(0.39)(0.4))

=((0.04-0.0312))/((0.04+0.1521-0.0624))

=0.0088/0.1297

=0.067848882

Weight B=1- Weight of Stock A

=1-0.067848882

=0.9321511

93.22% in stock B .

Answer:9 The proportion of optimal risky portfolio that should be invested in stock B:

Weight A =((0.21-0.05)(0.20)2 - (0.14-0.05)(0.20)(0.39)(0.4))/((0.21-0.05)(0.20)2 +(0.14-0.05)(0.39)2- (0.21-0.05+0.14-0.05)) (0.20)(0.39)(0.4))

=((0.0064-0.002808))/((0.0064+0.013689-0.0078))

=0.003592/0.012289

=0.292293921

Weight B=1- Weight of Stock A

=1-0.292293921

=0.707706

70.77% in stock B .

Answer:10 Expected return on the optimal risky portfolio:

=[(0.21*0.292293921+0.14*0.707706)]

=16.05%

Answer:11 Standard deviation of the optimal portfolio is:

2 = (.292293921)2 (0.39)2 + (0.707706)2 (0.20)2 + 2 (.292293921) (.707706) (0.39) (0.20) (0.4)

2 = 0.012994775+0.020033911 + 0.012907949 = 0.045936635

Standard deviation = square root of 0.045936635

=0.214328

or 21.43%

Answer:12 =Rp-Rf/beta

Beta of stock A=0.39*0.4/0.214328=0.727856

=0.21-0.05/0.727856=21.98%

Beta of stock B= 0.20*0.4/0.214328=0.373259676

=0.14-0.05/0.373259676=24.11%

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