3. The following incomplete table is about the efficient frontier for two-stock portfolio. As a person who constructs the efficient frontier is not a sophisticated investor, he wants to roughly figure out the combination of the expected return and volatility of the portfolio with certain numbers of different proportion of asset mixes. Due to many mistakes he makes, the following parts cover the only correct parts in the table. Portfolio weight for... Stock A Stock B Expected return Volatility 1.20 -0.20 1.00 0.00 8% 10% 0.80 0.20 12% 0.60 0.40 0.40 0.60 0.80 0.20 0.00 -0.20 22% 28% 1.00 1.20 (a) [6 points] Complete the blank parts of the expected return and the volatility of the portfolio given the asset mixes of the two assets. (b) (5 points) The graph of the efficient frontier represents the form of parabola. And the vertex of parabola in the efficient frontier is called as the minimum variance portfolio. Calculate the asset mix of the portfolio weights of the stock A and stock B, the mix which represents the minimum variance portfolio. (Hint: Take the differentiation of the volatility of the 2-stock portfolio with respect to the unknown one particular portfolio weight.] (e) [3 points) Calculate the expected return and the volatility of the minimum vari- ance portfolio. (d) [4 points) Excluding the inefficient frontier, the person wants to find the tangent portfolios from the available asset mix when the risk-free lending rate and risk- free borrowing rate is different. It is assumed that the risk-free lending rate is 4%. Determine which asset mix of two stocks is constituted as the tangent portfolio when the risk-free lending rate is used. [Tip: You don't have to start from the asset mix (Stock A, Stock B) = (1.2,-0.2). Once you obtain the asset mix of the minimum variance portfolio from part (b) question, disregard the asset mixes of the inefficient frontier. Then proceed the process of this question.] (e) (4 points) This question is connected with part (d) question. It is assumed that the risk-free borrowing rate is 8%. Out of the available asset mix except the inefficient frontier, determine which asset mix of two stocks is constituted as the tangent portfolio when the risk-free borrowing rate is used. [Follow the same tip from previous part (d) question.] (f) [3 points) This question is continued from part (d) or (e) question. Consider an investor having $500,000. As his style of investment is conservative, he wants to invest half-and-half for risk-free asset and the tangent portfolio respectively. Calculate the expected return and the volatility of this investment. 3. The following incomplete table is about the efficient frontier for two-stock portfolio. As a person who constructs the efficient frontier is not a sophisticated investor, he wants to roughly figure out the combination of the expected return and volatility of the portfolio with certain numbers of different proportion of asset mixes. Due to many mistakes he makes, the following parts cover the only correct parts in the table. Portfolio weight for... Stock A Stock B Expected return Volatility 1.20 -0.20 1.00 0.00 8% 10% 0.80 0.20 12% 0.60 0.40 0.40 0.60 0.80 0.20 0.00 -0.20 22% 28% 1.00 1.20 (a) [6 points] Complete the blank parts of the expected return and the volatility of the portfolio given the asset mixes of the two assets. (b) (5 points) The graph of the efficient frontier represents the form of parabola. And the vertex of parabola in the efficient frontier is called as the minimum variance portfolio. Calculate the asset mix of the portfolio weights of the stock A and stock B, the mix which represents the minimum variance portfolio. (Hint: Take the differentiation of the volatility of the 2-stock portfolio with respect to the unknown one particular portfolio weight.] (e) [3 points) Calculate the expected return and the volatility of the minimum vari- ance portfolio. (d) [4 points) Excluding the inefficient frontier, the person wants to find the tangent portfolios from the available asset mix when the risk-free lending rate and risk- free borrowing rate is different. It is assumed that the risk-free lending rate is 4%. Determine which asset mix of two stocks is constituted as the tangent portfolio when the risk-free lending rate is used. [Tip: You don't have to start from the asset mix (Stock A, Stock B) = (1.2,-0.2). Once you obtain the asset mix of the minimum variance portfolio from part (b) question, disregard the asset mixes of the inefficient frontier. Then proceed the process of this question.] (e) (4 points) This question is connected with part (d) question. It is assumed that the risk-free borrowing rate is 8%. Out of the available asset mix except the inefficient frontier, determine which asset mix of two stocks is constituted as the tangent portfolio when the risk-free borrowing rate is used. [Follow the same tip from previous part (d) question.] (f) [3 points) This question is continued from part (d) or (e) question. Consider an investor having $500,000. As his style of investment is conservative, he wants to invest half-and-half for risk-free asset and the tangent portfolio respectively. Calculate the expected return and the volatility of this investment