Give clear workings and explanation:

Question 2: (15 marks) A market consists of four stocks. The following information is given: Stock 1: r1=5%,1=10% Stock2: r2=10%,2=20% Stock 3:r3=15%,3=30% Stock 4:r4=20%,4=40% 12=13=14=0.6 Returns of Stock 2, Stock 3 and Stock 4 are independent of each other. Let P be a portfolio of the three stocks with weights (w1,w2,w3,w4) respectively. Let P denote the risk of such a portfolio. a) Given the information above, write down the expression for p2/2 by using the numerical values of the returns, risks and correlations given. (3 marks) b) Your client wants a portfolio with expected return of 35% and the lowest possible risk. Write down the Lagrangian needed for the optimization calculation based on the expression you got in Part a) (2 marks)