Question 2. (47 marks) Suppose you are given the following information about assets currently traded in the market. Standard deviation Expected return 10% 15% 0,2 B 0,3 0,4 Rf 25% 5% Correlation matrix: R(A) 1 0.2 0.4 0 R(A) R(B) R(C) Rf R(B) 0.2 1 0.8 0 R(C) 0.4 0.8 1 0 [48 Rf 0 0 0 1 a) Find the expected return and standard deviation of a tangency portfolio, which consists of the abovementioned assets (20 points) b) Derive the equation of CML (3 points) c) Construct an optimal portfolio made of a risk free asset and a tangency portfolio given the following utility function: Ui = 0.5 *E(RI) - 0,025*K*(gi)^2, where E(Ri) is the expected return of the optimal portfolio; K is the risk aversion coefficient equal to 10 for our investor; ci is the standard deviation of the optimal portfolio. Determine the weights of all assets comprising the optimal portfolio. (14 points) Question 2. (47 marks) Suppose you are given the following information about assets currently traded in the market. Standard deviation Expected return 10% 15% 0,2 B 0,3 0,4 Rf 25% 5% Correlation matrix: R(A) 1 0.2 0.4 0 R(A) R(B) R(C) Rf R(B) 0.2 1 0.8 0 R(C) 0.4 0.8 1 0 [48 Rf 0 0 0 1 a) Find the expected return and standard deviation of a tangency portfolio, which consists of the abovementioned assets (20 points) b) Derive the equation of CML (3 points) c) Construct an optimal portfolio made of a risk free asset and a tangency portfolio given the following utility function: Ui = 0.5 *E(RI) - 0,025*K*(gi)^2, where E(Ri) is the expected return of the optimal portfolio; K is the risk aversion coefficient equal to 10 for our investor; ci is the standard deviation of the optimal portfolio. Determine the weights of all assets comprising the optimal portfolio. (14 points)