Consider the case of three assets (A,B, and C). The corresponding expected returns are =0.070.100.06 and the correlation matrix is =10.50.40.510.50.40.51. The return variances of the asset returns are A2=0.04,B2=0.09,C2=0.04. The risk-free rate is rf=0.02. a) Determine the covariance matrix. b) For a required expected return =0.09, determine the portfolio return volatility as a square root of a polynomial function of C. (For this subquestion, do not use matrix notation) c) For a required expected return =0.09, determine the portfolio weights and the volatility of the portfolio with the lowest return volatility. (For this subquestion, do not use matrix notation) 1 d) Generalize your finding in c) for a general required expected return and use it obtain the volatility of the overall minimum variance portfolio. (For this subquestion, do not use matrix notation) e) Agent 1 has the preference PF0.5PF2. Calculate the optimal investment in the risky assets. f) Determine agent 1's optimal investment in the risk-free asset and determine the portfolio weights of the tangency portfolio. g) Provide the formula for the capital market line. h) Determine the risk-aversion coefficient b2 of the agent 2 , who holds the tangency portfolio exactly. i) The price vector of the assets is p=(50,100,200)T. How many units of each asset does investor 1 hold, if his/her total wealth is 1000 EUR. k) In total there are 4 investors in the economy, each having 1000 EUR wealth. The net investment in the risk-free asset is 1000 EUR. Calculate the market capitalization of each of the three risky assets