Consider a market with n risky assets and one risk-free asset. The investor constructs the portfolio...

  

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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 where Hpw' (1r)+rf, = w'w, 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: max W U (rp) = Hp - A0%, (1) 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: W = ( - 1). (2) 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 where Hpw' (1r)+rf, = w'w, 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: max W U (rp) = Hp - A0%, (1) 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: W = ( - 1). (2)