We now consider the mean-variance portfolio problem. As an investor, you can invest in the risk free asset, whose risk-free rate is 19= 2%, as well as in two risky assets j={A,B), which are characterized by the following variance-covariance matrix: Cov(A, B) COU(A, B) of These two assets have different expected return, given by E[ra] and E[r], respectively. You want to form an efficient mean-variance portfolio with the available assets respecting the budget constraint (wa + WB + Wif =1). The goal is thus to determine an allocation that minimizes the variance of portfolio returns under a target expected return constraint E[rp]>m. A) Write the Lagrangian function of the portfolio choice optimization problem, using y as the multiplier associated with the expected return constraint and uz as the one associated with the budget constraint. B) What are the optimal weights Wa and WB of the risky assets when these assets are independent of each other? C) What are the optimal weights Wa and Wp of the risky assets when these assets are positively correlated with each other, i.e. with a correlation p>0? Compare the difference with the case of p=0. D) Consider now the following environment: E[ra]=10%, E[TB]=15%, OA+OB=10%, p=0, 15%. Determine the portfolio weights of an efficient mean-variance portfolio that generates a target return of 18%. Interpret the results. We now consider the mean-variance portfolio problem. As an investor, you can invest in the risk free asset, whose risk-free rate is 19= 2%, as well as in two risky assets j={A,B), which are characterized by the following variance-covariance matrix: Cov(A, B) COU(A, B) of These two assets have different expected return, given by E[ra] and E[r], respectively. You want to form an efficient mean-variance portfolio with the available assets respecting the budget constraint (wa + WB + Wif =1). The goal is thus to determine an allocation that minimizes the variance of portfolio returns under a target expected return constraint E[rp]>m. A) Write the Lagrangian function of the portfolio choice optimization problem, using y as the multiplier associated with the expected return constraint and uz as the one associated with the budget constraint. B) What are the optimal weights Wa and WB of the risky assets when these assets are independent of each other? C) What are the optimal weights Wa and Wp of the risky assets when these assets are positively correlated with each other, i.e. with a correlation p>0? Compare the difference with the case of p=0. D) Consider now the following environment: E[ra]=10%, E[TB]=15%, OA+OB=10%, p=0, 15%. Determine the portfolio weights of an efficient mean-variance portfolio that generates a target return of 18%. Interpret the results