Consider a portfolio optimization problem without short selling for n = 3 risky securities with correlations, p12 = 0.10, p13 = 0.20, and p23 = 0.25. Following Markowitz's critical line method, the problem can be solved as MAX: .?I. 21:12:00 + E?=1E?=1xtxjaij 3T. ?:1Ii=1 xi 30 Expected returns and standard deviations are given by #1 0.10 01 0.20 ,0;- = 0.20 (:2 = 0.18 03 0.1-5 .03 0.12 For this portfolio problem, the efficient frontier can be constructed in a small number of steps. Note A is being used here in place of the It as per the lecture notes. Some partial results are as follows: Step 1: $1 = -0.05760 + 0.10000A 52 = 02 + bz $3 = 0.05040 + 0.080001 Step 2: 51 = 0.02523 + 0.04862A 52 = 0.42202 + 0.91743 53 = 03 + bgil Step 3: 51 = 01 + by) $2 = 0.32642 + 1.10166A $3 = 0.40639 0.586771 where s; is either x: or 6:(a slack variable) depending on whether the security is included in or excluded from the portfolio. Note that the conditions x,- 2 0, 6,- 2 0, and x,- 6; 2 0 must be satisfied a) Fill in the 6 missing numbers represented by, or, and b; for i = 1,2,3. Indicate whether each s,- is a x,- or a 6;. (6 marks). b) Identify all critical values of A. Between two adjacent critical A's (including A = 0), indicate which of the three securities are included in the portfolios along the efficient frontier. (6 marks)