Problem 1 (20%) Consider a market with n risky assets and one risk-free asset. The investor constructs the portfolio of all available assets. The portfolio mean return and variance are given by Mp = w' (u 1rf) +rf, om = w'w, = where u is the vector of mean returns of the risky assets, is the variance-covariance matrix, rf is the risk-free rate of return, and w is the vector of risky asset weights in the portfolio. The investor is the mean-variance utility maximizer and, hence, the investor's goal is: 1 max W U(rp) = Hp - AO (1) 2 where A is the investor's risk aversion coefficient. a) Solve the investor's utility maximization problem and show that the composi- tion of the optimal risky portfolio is given by: -1 W = '( - 1r;). (2) Problem 1 (20%) Consider a market with n risky assets and one risk-free asset. The investor constructs the portfolio of all available assets. The portfolio mean return and variance are given by Mp = w' (u 1rf) +rf, om = w'w, = where u is the vector of mean returns of the risky assets, is the variance-covariance matrix, rf is the risk-free rate of return, and w is the vector of risky asset weights in the portfolio. The investor is the mean-variance utility maximizer and, hence, the investor's goal is: 1 max W U(rp) = Hp - AO (1) 2 where A is the investor's risk aversion coefficient. a) Solve the investor's utility maximization problem and show that the composi- tion of the optimal risky portfolio is given by: -1 W = '( - 1r;). (2)